Av(13452, 13542, 14352, 31452, 31542, 34152, 41352, 43152)
Counting Sequence
1, 1, 2, 6, 24, 112, 570, 3058, 17002, 97020, 564796, 3340518, 20015220, 121224654, 740946160, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(2 x -1\right) F \left(x
\right)^{6}+\left(-8 x^{3}+4 x^{2}-11 x +7\right) F \left(x
\right)^{5}+\left(8 x^{5}-4 x^{4}+34 x^{3}-11 x^{2}+20 x -19\right) F \left(x
\right)^{4}+\left(-12 x^{5}+12 x^{4}-57 x^{3}-5 x^{2}-7 x +25\right) F \left(x
\right)^{3}+\left(-16 x^{4}+68 x^{3}+28 x^{2}-16 x -16\right) F \left(x
\right)^{2}+\left(-44 x^{3}-20 x^{2}+16 x +4\right) F \! \left(x \right)+4 x \left(x +1\right) \left(2 x -1\right) = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 570\)
\(\displaystyle a(7) = 3058\)
\(\displaystyle a(8) = 17002\)
\(\displaystyle a(9) = 97020\)
\(\displaystyle a(10) = 564796\)
\(\displaystyle a(11) = 3340518\)
\(\displaystyle a(12) = 20015220\)
\(\displaystyle a(13) = 121224654\)
\(\displaystyle a(14) = 740946160\)
\(\displaystyle a(15) = 4564407832\)
\(\displaystyle a(16) = 28309656448\)
\(\displaystyle a(17) = 176633015664\)
\(\displaystyle a(18) = 1107886916914\)
\(\displaystyle a(19) = 6981590203840\)
\(\displaystyle a(20) = 44181163905146\)
\(\displaystyle a(21) = 280649229246294\)
\(\displaystyle a(22) = 1788874996938738\)
\(\displaystyle a(23) = 11438050137161868\)
\(\displaystyle a(24) = 73343823860666178\)
\(\displaystyle a(25) = 471533706899675834\)
\(\displaystyle a(26) = 3038853614680030282\)
\(\displaystyle a(27) = 19627957938740419714\)
\(\displaystyle a(28) = 127039263218948395886\)
\(\displaystyle a(29) = 823825135080851694314\)
\(\displaystyle a(30) = 5351918965319363554704\)
\(\displaystyle a(31) = 34826534075096737241328\)
\(\displaystyle a(32) = 226981748869145382844548\)
\(\displaystyle a(33) = 1481527064168739491839458\)
\(\displaystyle a(34) = 9683402918863975628377000\)
\(\displaystyle a(35) = 63374027482445147070424032\)
\(\displaystyle a(36) = 415267165215545879123147320\)
\(\displaystyle a(37) = 2724253897274345533816988814\)
\(\displaystyle a(38) = 17891400743818818267276789246\)
\(\displaystyle a(39) = 117623218553337839374491239476\)
\(\displaystyle a(40) = 774053175259410061683581955706\)
\(\displaystyle a(41) = 5098663247299010643441017313640\)
\(\displaystyle a(42) = 33614756361888341961073684474796\)
\(\displaystyle a(43) = 221806065509891291960834294275248\)
\(\displaystyle a(44) = 1464770719116019753807310839264324\)
\(\displaystyle a(45) = 9680611317266401735011177290531730\)
\(\displaystyle a(46) = 64026238567828253718825368359144310\)
\(\displaystyle a(47) = 423761399478651669084025265148775084\)
\(\displaystyle a(48) = 2806596677768621535354932883688318602\)
\(\displaystyle a(49) = 18600372341920800302844464195353085268\)
\(\displaystyle a(50) = 123348774643276742387395275662312777988\)
\(\displaystyle a(51) = 818481456150137700253319600702715638298\)
\(\displaystyle a(52) = 5434173665233378762029894846778135463384\)
\(\displaystyle a(53) = 36099342212772623922013527662316141168130\)
\(\displaystyle a(54) = 239936957417129992137991500908269359032096\)
\(\displaystyle a(55) = 1595579933025260702930465571789700970541398\)
\(\displaystyle a(56) = 10615867281240714950291350198520379828443684\)
\(\displaystyle a(57) = 70664331836069652559949586629890741385747212\)
\(\displaystyle a(58) = 470593213130226502479533518616553066906990988\)
\(\displaystyle a(59) = 3135341306971022150756023049260836566954208296\)
\(\displaystyle a(60) = 20898313176960010738827745173284797368167240048\)
\(\displaystyle a(61) = 139353760322227720595828193368703284136511538664\)
\(\displaystyle a(62) = 929611119213436021782680208336283265970265545520\)
\(\displaystyle a(63) = 6203738413273313239372003744503196613227186400546\)
\(\displaystyle a(64) = 41416162009057429853223155688008999988397389181516\)
\(\displaystyle a(65) = 276595644029450326407776831700557842573526243961588\)
\(\displaystyle a(66) = 1847885563206251171752879080406667847545638751431946\)
\(\displaystyle a(67) = 12349643409701084636593407144518774241126350341282970\)
\(\displaystyle a(68) = 82561758938341664668254870261593604747756806363505954\)
\(\displaystyle a(69) = 552133869716989966343034770889139283763682637572359522\)
\(\displaystyle a(70) = 3693573254136488497366403062756746009452606167321901028\)
\(\displaystyle a(71) = 24716219031327647084551471295749602857363160309570162566\)
\(\displaystyle a(72) = 165442324249230265083817849144172586975409941021289966084\)
\(\displaystyle a(73) = 1107737636929286810327199212585367063757589343133774895422\)
\(\displaystyle a{\left(n + 74 \right)} = \frac{38329679771253964800 n \left(n - 2\right) \left(n - 1\right) \left(3 n + 2\right) \left(3 n + 4\right) a{\left(n \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{9997308234547200 n \left(n - 1\right) \left(276682 n^{3} + 1592358 n^{2} + 2675456 n + 1351899\right) a{\left(n + 1 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{47606229688320 n \left(164748337 n^{4} + 1501844567 n^{3} + 5298878517 n^{2} + 7682753362 n + 3712830215\right) a{\left(n + 2 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(982 n^{2} + 142415 n + 5162763\right) a{\left(n + 73 \right)}}{16 \left(n + 74\right) \left(2 n + 147\right)} + \frac{\left(72278 n^{4} + 19497319 n^{3} + 1966299502 n^{2} + 87832952861 n + 1465623326280\right) a{\left(n + 72 \right)}}{64 \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{5 \left(6030478 n^{5} + 2099718953 n^{4} + 292389186908 n^{3} + 20354504403907 n^{2} + 708365083154226 n + 9859147664201064\right) a{\left(n + 71 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{15 \left(223499912 n^{5} + 71611522195 n^{4} + 9141166703926 n^{3} + 580766845057953 n^{2} + 18352166135234726 n + 230557877008930344\right) a{\left(n + 69 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(246020506 n^{5} + 85502053115 n^{4} + 11884419730700 n^{3} + 825820601129965 n^{2} + 28687968317104374 n + 398575173440604060\right) a{\left(n + 70 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3967185807360 \left(4624338521 n^{5} + 49528826161 n^{4} + 262535757501 n^{3} + 758139204061 n^{2} + 1031198154460 n + 490717058260\right) a{\left(n + 3 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{73466403840 \left(528436222847 n^{5} + 16807374219163 n^{4} + 162563135785645 n^{3} + 684684137362013 n^{2} + 1314269390748288 n + 938246553651060\right) a{\left(n + 4 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(533806014371 n^{5} + 176485120436455 n^{4} + 23331228256721275 n^{3} + 1541616252851008865 n^{2} + 50911756086781669794 n + 672274388568385488600\right) a{\left(n + 68 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(2015863959748 n^{5} + 662469095532023 n^{4} + 87062222949861662 n^{3} + 5719537908824104225 n^{2} + 187826298530503530318 n + 2466625331455899144624\right) a{\left(n + 67 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(15051711748827 n^{5} + 4940404255570550 n^{4} + 648351263634282205 n^{3} + 42524657335344758810 n^{2} + 1393974858238265499748 n + 18270210646755799552380\right) a{\left(n + 66 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{6122200320 \left(76859892886571 n^{5} + 2209743835478035 n^{4} + 24516527458053735 n^{3} + 130618910861826941 n^{2} + 333808693098015622 n + 327523196147431800\right) a{\left(n + 5 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(108819656650739 n^{5} + 25490218051719160 n^{4} + 2081179572136872145 n^{3} + 58435750387256398460 n^{2} - 493772534041134107544 n - 36196216443543561747480\right) a{\left(n + 65 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3061100160 \left(220032002173393 n^{5} + 6220296234552005 n^{4} + 72359357555792981 n^{3} + 428799790047452091 n^{2} + 1279186131398762178 n + 1520033881329259000\right) a{\left(n + 6 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{170061120 \left(3083484076494659 n^{5} + 255910999916545213 n^{4} + 5481290158255718779 n^{3} + 49836055257985316891 n^{2} + 206710250037454440690 n + 322523338069269363960\right) a{\left(n + 7 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(6766092278633731 n^{5} + 2073321017620835255 n^{4} + 253964410891558962383 n^{3} + 15543766614902455639825 n^{2} + 475341263938466250700182 n + 5810301079672015077077808\right) a{\left(n + 64 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{28343520 \left(42477796590490723 n^{5} + 2933804198035808081 n^{4} + 66506646505260125307 n^{3} + 680705262886243801735 n^{2} + 3261669313167271918850 n + 5958365118828619911240\right) a{\left(n + 8 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(153220531695441338 n^{5} + 46717501917317867935 n^{4} + 5696256646125279875530 n^{3} + 347180343519099236366885 n^{2} + 10577296436108478702998952 n + 128865446692141358476530000\right) a{\left(n + 63 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(902132867670108587 n^{5} + 272008140133422381205 n^{4} + 32801047303872014449900 n^{3} + 1977413784996364922169200 n^{2} + 59595170373644623585352988 n + 718319840911175396062286820\right) a{\left(n + 62 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{4723920 \left(1429552800342211891 n^{5} + 36513804313662185579 n^{4} + 190105519168236845303 n^{3} - 2094041266853613795803 n^{2} - 24439087205960619137370 n - 66911542316427155657472\right) a{\left(n + 9 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{787320 \left(28955580160718364767 n^{5} + 1049485900866307170907 n^{4} + 13414750596027478341523 n^{3} + 62874002784767299396805 n^{2} - 16324534497137883418050 n - 636207681696505510894704\right) a{\left(n + 10 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(47432855961716409161 n^{5} + 13932220968965719534093 n^{4} + 1636806023220434917955959 n^{3} + 96143507664755177782239899 n^{2} + 2823505891087272641272995828 n + 33166031920014257777071838340\right) a{\left(n + 60 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(65047686710612029889 n^{5} + 19363508741346631741375 n^{4} + 2305448887868877864019465 n^{3} + 137232251303964931245675305 n^{2} + 4084003727637340130386860846 n + 48611086642217494047452996160\right) a{\left(n + 61 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{78732 \left(351837519158773485023 n^{5} + 14886646163826475264885 n^{4} + 235947348254777173250135 n^{3} + 1675414971830415689483795 n^{2} + 4687809914248271029839362 n + 1588043755202931317264400\right) a{\left(n + 11 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(954522057077003017029 n^{5} + 276613317635548385352485 n^{4} + 32063193488999219896101985 n^{3} + 1858219781485716021567128755 n^{2} + 53844831267161807826286103186 n + 624076186246550839280392783440\right) a{\left(n + 59 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(7199743888830282172387 n^{5} + 2059161527079980091518450 n^{4} + 235566458165711579161717085 n^{3} + 13473983659320074588494689010 n^{2} + 385334545692044053789167878748 n + 4407872850598659325940379696480\right) a{\left(n + 58 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(31914469936089198408526 n^{5} + 9798730011794111250622125 n^{4} + 1182733553423992116676324915 n^{3} + 70419659204965902187935583465 n^{2} + 2073705660850588133942740348569 n + 24209194302429979825107495015780\right) a{\left(n + 54 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{4374 \left(35304797256135605190341 n^{5} + 1797295549938969857061115 n^{4} + 35951838647367574989854125 n^{3} + 351090323540730785254605245 n^{2} + 1658431594105631516770459014 n + 2984452350408338081277954240\right) a{\left(n + 12 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{729 \left(41427068380592059164841 n^{5} + 1956685488109013113678925 n^{4} + 33098479239261245747299445 n^{3} + 218686161856436493821936035 n^{2} + 181710598801454442007788954 n - 2385863393159358429735070440\right) a{\left(n + 13 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(59736134922155820654427 n^{5} + 16878149137136348973034925 n^{4} + 1907432283591784766217673055 n^{3} + 107775443696945321533206951355 n^{2} + 3044644862735980084995370734198 n + 34402446239632620467050983902040\right) a{\left(n + 57 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{10935 \left(92508382227754139018501 n^{5} + 5688868648531551923259525 n^{4} + 138998803322247765837775809 n^{3} + 1683869141433574776434123867 n^{2} + 10092171339864116958825249426 n + 23872925290160322598009915656\right) a{\left(n + 14 \right)}}{2 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(98631541872286233174091 n^{5} + 27602354963552750979576875 n^{4} + 3089244302634413258795044625 n^{3} + 172840438178622430035817151725 n^{2} + 4834221567637789270630047578064 n + 54073795910659713683229000781620\right) a{\left(n + 56 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(154403578919895636101101 n^{5} + 43180549132060871242494135 n^{4} + 4826090149565310523815289625 n^{3} + 269468906069352634170805548345 n^{2} + 7517019859593855139343327278914 n + 83813296592280302227953010287960\right) a{\left(n + 55 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(292684507181452659611983 n^{5} + 71812452860700066655653374 n^{4} + 7013885283948937412887605089 n^{3} + 340618694563393837833182588086 n^{2} + 8217353507632973680902141566460 n + 78692568042115104541982889588144\right) a{\left(n + 53 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{405 \left(635168994765365790733525 n^{5} + 52431692778390099633996035 n^{4} + 1703894741784777587891950781 n^{3} + 27345091117115567915141451781 n^{2} + 217214357248810980595420135566 n + 684288065548828919748190784184\right) a{\left(n + 15 \right)}}{4 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(6821273583098406565576076 n^{5} + 1710036966647838416315117905 n^{4} + 171408448689744370118373555286 n^{3} + 8587264580177839694803701174263 n^{2} + 215016830305948232171544184582542 n + 2152653126828791673510913270745448\right) a{\left(n + 51 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(19164170758436633554785671 n^{5} + 4818981810582973451484217165 n^{4} + 484332314676500515879625903095 n^{3} + 24319204900144365571237276848635 n^{2} + 610037789073131610100154889499554 n + 6115583533643359307560454853048120\right) a{\left(n + 52 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{243 \left(36603819664344429021181571 n^{5} + 2611235948265791194550035185 n^{4} + 74276484392619012843803713015 n^{3} + 1052274963059358435085566020995 n^{2} + 7418093156040290311488034325594 n + 20794996875129487747363917776280\right) a{\left(n + 16 \right)}}{8 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{81 \left(53522569106211065570874467 n^{5} + 4636007725491941713677104395 n^{4} + 159790500388690880546384201495 n^{3} + 2743709851816001075103382754105 n^{2} + 23495309230736808019471632209138 n + 80334566341192147350531877106160\right) a{\left(n + 17 \right)}}{16 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(97250320645945198669885672 n^{5} + 24850322936821611102930369545 n^{4} + 2530654304876496151732602110990 n^{3} + 128432925490406855948287337036995 n^{2} + 3249439673019298649909981045768598 n + 32797680401967312659659156077778080\right) a{\left(n + 49 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(138278281029988559737962038 n^{5} + 28746203638175522937118539715 n^{4} + 2346140120782993879563079269040 n^{3} + 93369905748157704821910405173345 n^{2} + 1793203464910018381297572090767142 n + 13050878088802377619755367224186960\right) a{\left(n + 48 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(160151550483040494580407253 n^{5} + 40005023251982933875458746795 n^{4} + 3994708444375861283175801800405 n^{3} + 199325125125632756960677786601125 n^{2} + 4969972785161893891459139085218742 n + 49540346163618593152076179389098640\right) a{\left(n + 50 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(377806441779685009751906776 n^{5} + 84910258614361698748150369595 n^{4} + 7624149366766922048209901397390 n^{3} + 341852756744886264168097712788525 n^{2} + 7653599103224141275589687332984394 n + 68441522315009396116284282756615960\right) a{\left(n + 47 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{27 \left(1030188243963445072562898173 n^{5} + 101278163790102137014117235155 n^{4} + 3946663619081497458146431008685 n^{3} + 76414102134371753034976910125025 n^{2} + 736585966713592575844144315586322 n + 2832123877448997906494386411373640\right) a{\left(n + 19 \right)}}{64 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{27 \left(1299325522237765103292470473 n^{5} + 153292057621820136162058952495 n^{4} + 7044110405010116507160275695625 n^{3} + 159069260660113304529466075788265 n^{2} + 1775614608149455194099816082041102 n + 7868336807556975775390214493904920\right) a{\left(n + 21 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{27 \left(2240683261091194789576605989 n^{5} + 182280153004586161181998548145 n^{4} + 5922262713268328060377327501585 n^{3} + 96023077631861417589245306995115 n^{2} + 776627087735110408119984965435766 n + 2505309993753521547750617578824000\right) a{\left(n + 18 \right)}}{32 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(2271059498703014652251471961 n^{5} + 508898203580560867280037103275 n^{4} + 45585122687329962437186677493065 n^{3} + 2040368776867357099850535952653525 n^{2} + 45633170365279219888487110066582934 n + 407963861550971484357770587179864840\right) a{\left(n + 46 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(3362774693411588206443413851 n^{5} + 761076476973604212170386334185 n^{4} + 68617861337010408251268179541735 n^{3} + 3081892922617302094563160238597455 n^{2} + 68979940196856583135617846933417894 n + 615704991414473056818138841115577600\right) a{\left(n + 44 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{81 \left(4371130578651527608079083667 n^{5} + 403515343060789594956696419105 n^{4} + 14893056958433234152870454598215 n^{3} + 274687389075574132160859014943255 n^{2} + 2531496442980900504426834038669238 n + 9324627209053639826974786828464120\right) a{\left(n + 20 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{27 \left(5655139432266181365050226799 n^{5} + 601718492477200402962237363005 n^{4} + 25714351958854881866091521723715 n^{3} + 551248387424451167402292104639575 n^{2} + 5922300917641811355620275368854426 n + 25481916370239111810459145258656360\right) a{\left(n + 23 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(12371160549397587838802228129 n^{5} + 2750806201364243320041844114915 n^{4} + 244453546783768357337794940872345 n^{3} + 10852645813695815655512962739977085 n^{2} + 240703984381559679078519998862200166 n + 2133703354353159092855096229061857840\right) a{\left(n + 45 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(17975479133902570908002812219 n^{5} + 3531562809265568748847336426295 n^{4} + 276662258752286891808824695871615 n^{3} + 10799397345102867426312904026650185 n^{2} + 209966877859318573140022815236860566 n + 1625912871384354664020384817404341280\right) a{\left(n + 43 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(32650811459532707155611043693 n^{5} + 5476891595652562363129274432735 n^{4} + 362629882192328660107047480480785 n^{3} + 11804809653582240104525147528484145 n^{2} + 187957489744567897000942956143391882 n + 1161494186865138168196995822906816120\right) a{\left(n + 39 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{27 \left(35760470293793738399143745057 n^{5} + 3723312071192977920456692832415 n^{4} + 155146236028634107896361435925545 n^{3} + 3234479813194245984771311849564345 n^{2} + 33741947949287615591330848732968438 n + 140920566777667255808288836366754760\right) a{\left(n + 22 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(43037522547951009082203621502 n^{5} + 8646816258135124465163111000405 n^{4} + 694765101696833570254203281115200 n^{3} + 27906472102916854513508181011301655 n^{2} + 560350202363627436913545379414928958 n + 4499811798474721514627296489251510360\right) a{\left(n + 42 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(43458143739135618561667611643 n^{5} + 8496276857043683961947015042615 n^{4} + 663991478006247519245751856816100 n^{3} + 25929058517944900108134203331275785 n^{2} + 505946885824466346066691942511118087 n + 3946481929532285231399361975985222950\right) a{\left(n + 40 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(56700313723128059710113795527 n^{5} + 11241051880692924547712841309125 n^{4} + 891203143891363204101541081036515 n^{3} + 35318724599102457842244000659066355 n^{2} + 699668074290098868295101668118600758 n + 5542783948087784853117146197416689880\right) a{\left(n + 41 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(83456173136315621774470157429 n^{5} + 15424069120160695811007465359785 n^{4} + 1103923613685761770767490864378825 n^{3} + 38554293209970104773972090050247655 n^{2} + 660343836164158866525694037196135306 n + 4451793809290952082294401827470819720\right) a{\left(n + 33 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(107160812079206688701882214376 n^{5} + 19619093092183955515664225800280 n^{4} + 1435885197652965088921767414927245 n^{3} + 52512736044791763853022341050333550 n^{2} + 959643076333887286644024577578172509 n + 7010366188627064080205343735843425220\right) a{\left(n + 38 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(113340476487510843468918219043 n^{5} + 14573650020324376750669302416225 n^{4} + 668318633029330845796190791211555 n^{3} + 11662567389353045383068448994695495 n^{2} + 9272364941736290378783833339215882 n - 1224686816099384606197066213224410520\right) a{\left(n + 36 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{9 \left(141333028271381937993811773261 n^{5} + 17201843315050550333597347022165 n^{4} + 839293098779568755406793824080865 n^{3} + 20517329245593818915199488299856195 n^{2} + 251270235648482678960697755662144994 n + 1233117267037782310761558487660980120\right) a{\left(n + 25 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{15 \left(210160023586093082689203835683 n^{5} + 29281331257032527318993210792219 n^{4} + 1631606230581321209106486618327243 n^{3} + 45452283541221574920280171719907721 n^{2} + 633044713213760081785682437023918998 n + 3526666118354278204223570857359008208\right) a{\left(n + 29 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(301341785315965934240330877151 n^{5} + 54778148959477941920276064578960 n^{4} + 3976877574109704629271145110236285 n^{3} + 144141892635465490688296595845194820 n^{2} + 2608344666496546639860664350383576184 n + 18852445079582079424015739545030197000\right) a{\left(n + 37 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(421659680385280391421005188109 n^{5} + 62333342855983802148549932852475 n^{4} + 3692023833546944339377354302365845 n^{3} + 109518648430486717573185357894862365 n^{2} + 1626926885297515047253183474964164926 n + 9682000732135574740348456772607181320\right) a{\left(n + 30 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(424955339670930168926136013193 n^{5} + 70123552422201061879525138426390 n^{4} + 4625805110547840989063430174894145 n^{3} + 152485896865480371717522572789614610 n^{2} + 2511877266629727741516648648854078802 n + 16542169300278634730295456893176772400\right) a{\left(n + 35 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{5 \left(444947888099083117347087662336 n^{5} + 65599192907249650958534488229971 n^{4} + 3865705152601198865318577621951382 n^{3} + 113817741560313362541886441772779133 n^{2} + 1674337830054829926745498661500852146 n + 9845091953398618236945027964740331656\right) a{\left(n + 31 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(622864787300745772699570589579 n^{5} + 81828658624822474125153497352280 n^{4} + 4301959949182925626090775503268260 n^{3} + 113138517241122141735838281447835055 n^{2} + 1488534823345478445774045378603110196 n + 7838272143509801325000338247607872360\right) a{\left(n + 27 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(786804455430625864856576135971 n^{5} + 98225734592572928935357306184345 n^{4} + 4901567174985675639595388400872875 n^{3} + 122224152503320760210407311451875055 n^{2} + 1523149324981873934118706864116963154 n + 7589823981533533842727220008623572280\right) a{\left(n + 26 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(801556854028467394171913165917 n^{5} + 92384287596150665728546625303735 n^{4} + 4260992956202609435702752004339285 n^{3} + 98322191966431671266877734909591305 n^{2} + 1135234426817193416093840578372531878 n + 5247628997968585680632057477046569400\right) a{\left(n + 24 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(2444757122469580022392018669987 n^{5} + 397933881739632725925974230305725 n^{4} + 25886059008196819549996933963606475 n^{3} + 841216249404751424343400123588331635 n^{2} + 13656287547691131798949430496744034338 n + 88598668432369517245079098605756974880\right) a{\left(n + 34 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(2608923675906521184772727332043 n^{5} + 343592048447632100548406204583985 n^{4} + 18055146636340492285787907878497915 n^{3} + 473140007621294108199267562538042375 n^{2} + 6182233967087156797850000323469282442 n + 32216972939158600442096141908427040600\right) a{\left(n + 28 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(3950947268585902088537549783681 n^{5} + 600060071952837038416058762154895 n^{4} + 36453635302543070569511692940728345 n^{3} + 1107315092283070784876152409883315665 n^{2} + 16819352866229369368883599677710929494 n + 102204550744546047204730860841050215280\right) a{\left(n + 32 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)}, \quad n \geq 74\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 570\)
\(\displaystyle a(7) = 3058\)
\(\displaystyle a(8) = 17002\)
\(\displaystyle a(9) = 97020\)
\(\displaystyle a(10) = 564796\)
\(\displaystyle a(11) = 3340518\)
\(\displaystyle a(12) = 20015220\)
\(\displaystyle a(13) = 121224654\)
\(\displaystyle a(14) = 740946160\)
\(\displaystyle a(15) = 4564407832\)
\(\displaystyle a(16) = 28309656448\)
\(\displaystyle a(17) = 176633015664\)
\(\displaystyle a(18) = 1107886916914\)
\(\displaystyle a(19) = 6981590203840\)
\(\displaystyle a(20) = 44181163905146\)
\(\displaystyle a(21) = 280649229246294\)
\(\displaystyle a(22) = 1788874996938738\)
\(\displaystyle a(23) = 11438050137161868\)
\(\displaystyle a(24) = 73343823860666178\)
\(\displaystyle a(25) = 471533706899675834\)
\(\displaystyle a(26) = 3038853614680030282\)
\(\displaystyle a(27) = 19627957938740419714\)
\(\displaystyle a(28) = 127039263218948395886\)
\(\displaystyle a(29) = 823825135080851694314\)
\(\displaystyle a(30) = 5351918965319363554704\)
\(\displaystyle a(31) = 34826534075096737241328\)
\(\displaystyle a(32) = 226981748869145382844548\)
\(\displaystyle a(33) = 1481527064168739491839458\)
\(\displaystyle a(34) = 9683402918863975628377000\)
\(\displaystyle a(35) = 63374027482445147070424032\)
\(\displaystyle a(36) = 415267165215545879123147320\)
\(\displaystyle a(37) = 2724253897274345533816988814\)
\(\displaystyle a(38) = 17891400743818818267276789246\)
\(\displaystyle a(39) = 117623218553337839374491239476\)
\(\displaystyle a(40) = 774053175259410061683581955706\)
\(\displaystyle a(41) = 5098663247299010643441017313640\)
\(\displaystyle a(42) = 33614756361888341961073684474796\)
\(\displaystyle a(43) = 221806065509891291960834294275248\)
\(\displaystyle a(44) = 1464770719116019753807310839264324\)
\(\displaystyle a(45) = 9680611317266401735011177290531730\)
\(\displaystyle a(46) = 64026238567828253718825368359144310\)
\(\displaystyle a(47) = 423761399478651669084025265148775084\)
\(\displaystyle a(48) = 2806596677768621535354932883688318602\)
\(\displaystyle a(49) = 18600372341920800302844464195353085268\)
\(\displaystyle a(50) = 123348774643276742387395275662312777988\)
\(\displaystyle a(51) = 818481456150137700253319600702715638298\)
\(\displaystyle a(52) = 5434173665233378762029894846778135463384\)
\(\displaystyle a(53) = 36099342212772623922013527662316141168130\)
\(\displaystyle a(54) = 239936957417129992137991500908269359032096\)
\(\displaystyle a(55) = 1595579933025260702930465571789700970541398\)
\(\displaystyle a(56) = 10615867281240714950291350198520379828443684\)
\(\displaystyle a(57) = 70664331836069652559949586629890741385747212\)
\(\displaystyle a(58) = 470593213130226502479533518616553066906990988\)
\(\displaystyle a(59) = 3135341306971022150756023049260836566954208296\)
\(\displaystyle a(60) = 20898313176960010738827745173284797368167240048\)
\(\displaystyle a(61) = 139353760322227720595828193368703284136511538664\)
\(\displaystyle a(62) = 929611119213436021782680208336283265970265545520\)
\(\displaystyle a(63) = 6203738413273313239372003744503196613227186400546\)
\(\displaystyle a(64) = 41416162009057429853223155688008999988397389181516\)
\(\displaystyle a(65) = 276595644029450326407776831700557842573526243961588\)
\(\displaystyle a(66) = 1847885563206251171752879080406667847545638751431946\)
\(\displaystyle a(67) = 12349643409701084636593407144518774241126350341282970\)
\(\displaystyle a(68) = 82561758938341664668254870261593604747756806363505954\)
\(\displaystyle a(69) = 552133869716989966343034770889139283763682637572359522\)
\(\displaystyle a(70) = 3693573254136488497366403062756746009452606167321901028\)
\(\displaystyle a(71) = 24716219031327647084551471295749602857363160309570162566\)
\(\displaystyle a(72) = 165442324249230265083817849144172586975409941021289966084\)
\(\displaystyle a(73) = 1107737636929286810327199212585367063757589343133774895422\)
\(\displaystyle a{\left(n + 74 \right)} = \frac{38329679771253964800 n \left(n - 2\right) \left(n - 1\right) \left(3 n + 2\right) \left(3 n + 4\right) a{\left(n \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{9997308234547200 n \left(n - 1\right) \left(276682 n^{3} + 1592358 n^{2} + 2675456 n + 1351899\right) a{\left(n + 1 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{47606229688320 n \left(164748337 n^{4} + 1501844567 n^{3} + 5298878517 n^{2} + 7682753362 n + 3712830215\right) a{\left(n + 2 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(982 n^{2} + 142415 n + 5162763\right) a{\left(n + 73 \right)}}{16 \left(n + 74\right) \left(2 n + 147\right)} + \frac{\left(72278 n^{4} + 19497319 n^{3} + 1966299502 n^{2} + 87832952861 n + 1465623326280\right) a{\left(n + 72 \right)}}{64 \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{5 \left(6030478 n^{5} + 2099718953 n^{4} + 292389186908 n^{3} + 20354504403907 n^{2} + 708365083154226 n + 9859147664201064\right) a{\left(n + 71 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{15 \left(223499912 n^{5} + 71611522195 n^{4} + 9141166703926 n^{3} + 580766845057953 n^{2} + 18352166135234726 n + 230557877008930344\right) a{\left(n + 69 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(246020506 n^{5} + 85502053115 n^{4} + 11884419730700 n^{3} + 825820601129965 n^{2} + 28687968317104374 n + 398575173440604060\right) a{\left(n + 70 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3967185807360 \left(4624338521 n^{5} + 49528826161 n^{4} + 262535757501 n^{3} + 758139204061 n^{2} + 1031198154460 n + 490717058260\right) a{\left(n + 3 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{73466403840 \left(528436222847 n^{5} + 16807374219163 n^{4} + 162563135785645 n^{3} + 684684137362013 n^{2} + 1314269390748288 n + 938246553651060\right) a{\left(n + 4 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(533806014371 n^{5} + 176485120436455 n^{4} + 23331228256721275 n^{3} + 1541616252851008865 n^{2} + 50911756086781669794 n + 672274388568385488600\right) a{\left(n + 68 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(2015863959748 n^{5} + 662469095532023 n^{4} + 87062222949861662 n^{3} + 5719537908824104225 n^{2} + 187826298530503530318 n + 2466625331455899144624\right) a{\left(n + 67 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(15051711748827 n^{5} + 4940404255570550 n^{4} + 648351263634282205 n^{3} + 42524657335344758810 n^{2} + 1393974858238265499748 n + 18270210646755799552380\right) a{\left(n + 66 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{6122200320 \left(76859892886571 n^{5} + 2209743835478035 n^{4} + 24516527458053735 n^{3} + 130618910861826941 n^{2} + 333808693098015622 n + 327523196147431800\right) a{\left(n + 5 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(108819656650739 n^{5} + 25490218051719160 n^{4} + 2081179572136872145 n^{3} + 58435750387256398460 n^{2} - 493772534041134107544 n - 36196216443543561747480\right) a{\left(n + 65 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3061100160 \left(220032002173393 n^{5} + 6220296234552005 n^{4} + 72359357555792981 n^{3} + 428799790047452091 n^{2} + 1279186131398762178 n + 1520033881329259000\right) a{\left(n + 6 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{170061120 \left(3083484076494659 n^{5} + 255910999916545213 n^{4} + 5481290158255718779 n^{3} + 49836055257985316891 n^{2} + 206710250037454440690 n + 322523338069269363960\right) a{\left(n + 7 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(6766092278633731 n^{5} + 2073321017620835255 n^{4} + 253964410891558962383 n^{3} + 15543766614902455639825 n^{2} + 475341263938466250700182 n + 5810301079672015077077808\right) a{\left(n + 64 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{28343520 \left(42477796590490723 n^{5} + 2933804198035808081 n^{4} + 66506646505260125307 n^{3} + 680705262886243801735 n^{2} + 3261669313167271918850 n + 5958365118828619911240\right) a{\left(n + 8 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(153220531695441338 n^{5} + 46717501917317867935 n^{4} + 5696256646125279875530 n^{3} + 347180343519099236366885 n^{2} + 10577296436108478702998952 n + 128865446692141358476530000\right) a{\left(n + 63 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(902132867670108587 n^{5} + 272008140133422381205 n^{4} + 32801047303872014449900 n^{3} + 1977413784996364922169200 n^{2} + 59595170373644623585352988 n + 718319840911175396062286820\right) a{\left(n + 62 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{4723920 \left(1429552800342211891 n^{5} + 36513804313662185579 n^{4} + 190105519168236845303 n^{3} - 2094041266853613795803 n^{2} - 24439087205960619137370 n - 66911542316427155657472\right) a{\left(n + 9 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{787320 \left(28955580160718364767 n^{5} + 1049485900866307170907 n^{4} + 13414750596027478341523 n^{3} + 62874002784767299396805 n^{2} - 16324534497137883418050 n - 636207681696505510894704\right) a{\left(n + 10 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(47432855961716409161 n^{5} + 13932220968965719534093 n^{4} + 1636806023220434917955959 n^{3} + 96143507664755177782239899 n^{2} + 2823505891087272641272995828 n + 33166031920014257777071838340\right) a{\left(n + 60 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(65047686710612029889 n^{5} + 19363508741346631741375 n^{4} + 2305448887868877864019465 n^{3} + 137232251303964931245675305 n^{2} + 4084003727637340130386860846 n + 48611086642217494047452996160\right) a{\left(n + 61 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{78732 \left(351837519158773485023 n^{5} + 14886646163826475264885 n^{4} + 235947348254777173250135 n^{3} + 1675414971830415689483795 n^{2} + 4687809914248271029839362 n + 1588043755202931317264400\right) a{\left(n + 11 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(954522057077003017029 n^{5} + 276613317635548385352485 n^{4} + 32063193488999219896101985 n^{3} + 1858219781485716021567128755 n^{2} + 53844831267161807826286103186 n + 624076186246550839280392783440\right) a{\left(n + 59 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(7199743888830282172387 n^{5} + 2059161527079980091518450 n^{4} + 235566458165711579161717085 n^{3} + 13473983659320074588494689010 n^{2} + 385334545692044053789167878748 n + 4407872850598659325940379696480\right) a{\left(n + 58 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(31914469936089198408526 n^{5} + 9798730011794111250622125 n^{4} + 1182733553423992116676324915 n^{3} + 70419659204965902187935583465 n^{2} + 2073705660850588133942740348569 n + 24209194302429979825107495015780\right) a{\left(n + 54 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{4374 \left(35304797256135605190341 n^{5} + 1797295549938969857061115 n^{4} + 35951838647367574989854125 n^{3} + 351090323540730785254605245 n^{2} + 1658431594105631516770459014 n + 2984452350408338081277954240\right) a{\left(n + 12 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{729 \left(41427068380592059164841 n^{5} + 1956685488109013113678925 n^{4} + 33098479239261245747299445 n^{3} + 218686161856436493821936035 n^{2} + 181710598801454442007788954 n - 2385863393159358429735070440\right) a{\left(n + 13 \right)}}{\left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(59736134922155820654427 n^{5} + 16878149137136348973034925 n^{4} + 1907432283591784766217673055 n^{3} + 107775443696945321533206951355 n^{2} + 3044644862735980084995370734198 n + 34402446239632620467050983902040\right) a{\left(n + 57 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{10935 \left(92508382227754139018501 n^{5} + 5688868648531551923259525 n^{4} + 138998803322247765837775809 n^{3} + 1683869141433574776434123867 n^{2} + 10092171339864116958825249426 n + 23872925290160322598009915656\right) a{\left(n + 14 \right)}}{2 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(98631541872286233174091 n^{5} + 27602354963552750979576875 n^{4} + 3089244302634413258795044625 n^{3} + 172840438178622430035817151725 n^{2} + 4834221567637789270630047578064 n + 54073795910659713683229000781620\right) a{\left(n + 56 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(154403578919895636101101 n^{5} + 43180549132060871242494135 n^{4} + 4826090149565310523815289625 n^{3} + 269468906069352634170805548345 n^{2} + 7517019859593855139343327278914 n + 83813296592280302227953010287960\right) a{\left(n + 55 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(292684507181452659611983 n^{5} + 71812452860700066655653374 n^{4} + 7013885283948937412887605089 n^{3} + 340618694563393837833182588086 n^{2} + 8217353507632973680902141566460 n + 78692568042115104541982889588144\right) a{\left(n + 53 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{405 \left(635168994765365790733525 n^{5} + 52431692778390099633996035 n^{4} + 1703894741784777587891950781 n^{3} + 27345091117115567915141451781 n^{2} + 217214357248810980595420135566 n + 684288065548828919748190784184\right) a{\left(n + 15 \right)}}{4 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{5 \left(6821273583098406565576076 n^{5} + 1710036966647838416315117905 n^{4} + 171408448689744370118373555286 n^{3} + 8587264580177839694803701174263 n^{2} + 215016830305948232171544184582542 n + 2152653126828791673510913270745448\right) a{\left(n + 51 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(19164170758436633554785671 n^{5} + 4818981810582973451484217165 n^{4} + 484332314676500515879625903095 n^{3} + 24319204900144365571237276848635 n^{2} + 610037789073131610100154889499554 n + 6115583533643359307560454853048120\right) a{\left(n + 52 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{243 \left(36603819664344429021181571 n^{5} + 2611235948265791194550035185 n^{4} + 74276484392619012843803713015 n^{3} + 1052274963059358435085566020995 n^{2} + 7418093156040290311488034325594 n + 20794996875129487747363917776280\right) a{\left(n + 16 \right)}}{8 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{81 \left(53522569106211065570874467 n^{5} + 4636007725491941713677104395 n^{4} + 159790500388690880546384201495 n^{3} + 2743709851816001075103382754105 n^{2} + 23495309230736808019471632209138 n + 80334566341192147350531877106160\right) a{\left(n + 17 \right)}}{16 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(97250320645945198669885672 n^{5} + 24850322936821611102930369545 n^{4} + 2530654304876496151732602110990 n^{3} + 128432925490406855948287337036995 n^{2} + 3249439673019298649909981045768598 n + 32797680401967312659659156077778080\right) a{\left(n + 49 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(138278281029988559737962038 n^{5} + 28746203638175522937118539715 n^{4} + 2346140120782993879563079269040 n^{3} + 93369905748157704821910405173345 n^{2} + 1793203464910018381297572090767142 n + 13050878088802377619755367224186960\right) a{\left(n + 48 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(160151550483040494580407253 n^{5} + 40005023251982933875458746795 n^{4} + 3994708444375861283175801800405 n^{3} + 199325125125632756960677786601125 n^{2} + 4969972785161893891459139085218742 n + 49540346163618593152076179389098640\right) a{\left(n + 50 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(377806441779685009751906776 n^{5} + 84910258614361698748150369595 n^{4} + 7624149366766922048209901397390 n^{3} + 341852756744886264168097712788525 n^{2} + 7653599103224141275589687332984394 n + 68441522315009396116284282756615960\right) a{\left(n + 47 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{27 \left(1030188243963445072562898173 n^{5} + 101278163790102137014117235155 n^{4} + 3946663619081497458146431008685 n^{3} + 76414102134371753034976910125025 n^{2} + 736585966713592575844144315586322 n + 2832123877448997906494386411373640\right) a{\left(n + 19 \right)}}{64 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{27 \left(1299325522237765103292470473 n^{5} + 153292057621820136162058952495 n^{4} + 7044110405010116507160275695625 n^{3} + 159069260660113304529466075788265 n^{2} + 1775614608149455194099816082041102 n + 7868336807556975775390214493904920\right) a{\left(n + 21 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{27 \left(2240683261091194789576605989 n^{5} + 182280153004586161181998548145 n^{4} + 5922262713268328060377327501585 n^{3} + 96023077631861417589245306995115 n^{2} + 776627087735110408119984965435766 n + 2505309993753521547750617578824000\right) a{\left(n + 18 \right)}}{32 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(2271059498703014652251471961 n^{5} + 508898203580560867280037103275 n^{4} + 45585122687329962437186677493065 n^{3} + 2040368776867357099850535952653525 n^{2} + 45633170365279219888487110066582934 n + 407963861550971484357770587179864840\right) a{\left(n + 46 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(3362774693411588206443413851 n^{5} + 761076476973604212170386334185 n^{4} + 68617861337010408251268179541735 n^{3} + 3081892922617302094563160238597455 n^{2} + 68979940196856583135617846933417894 n + 615704991414473056818138841115577600\right) a{\left(n + 44 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{81 \left(4371130578651527608079083667 n^{5} + 403515343060789594956696419105 n^{4} + 14893056958433234152870454598215 n^{3} + 274687389075574132160859014943255 n^{2} + 2531496442980900504426834038669238 n + 9324627209053639826974786828464120\right) a{\left(n + 20 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{27 \left(5655139432266181365050226799 n^{5} + 601718492477200402962237363005 n^{4} + 25714351958854881866091521723715 n^{3} + 551248387424451167402292104639575 n^{2} + 5922300917641811355620275368854426 n + 25481916370239111810459145258656360\right) a{\left(n + 23 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(12371160549397587838802228129 n^{5} + 2750806201364243320041844114915 n^{4} + 244453546783768357337794940872345 n^{3} + 10852645813695815655512962739977085 n^{2} + 240703984381559679078519998862200166 n + 2133703354353159092855096229061857840\right) a{\left(n + 45 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(17975479133902570908002812219 n^{5} + 3531562809265568748847336426295 n^{4} + 276662258752286891808824695871615 n^{3} + 10799397345102867426312904026650185 n^{2} + 209966877859318573140022815236860566 n + 1625912871384354664020384817404341280\right) a{\left(n + 43 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(32650811459532707155611043693 n^{5} + 5476891595652562363129274432735 n^{4} + 362629882192328660107047480480785 n^{3} + 11804809653582240104525147528484145 n^{2} + 187957489744567897000942956143391882 n + 1161494186865138168196995822906816120\right) a{\left(n + 39 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{27 \left(35760470293793738399143745057 n^{5} + 3723312071192977920456692832415 n^{4} + 155146236028634107896361435925545 n^{3} + 3234479813194245984771311849564345 n^{2} + 33741947949287615591330848732968438 n + 140920566777667255808288836366754760\right) a{\left(n + 22 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(43037522547951009082203621502 n^{5} + 8646816258135124465163111000405 n^{4} + 694765101696833570254203281115200 n^{3} + 27906472102916854513508181011301655 n^{2} + 560350202363627436913545379414928958 n + 4499811798474721514627296489251510360\right) a{\left(n + 42 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(43458143739135618561667611643 n^{5} + 8496276857043683961947015042615 n^{4} + 663991478006247519245751856816100 n^{3} + 25929058517944900108134203331275785 n^{2} + 505946885824466346066691942511118087 n + 3946481929532285231399361975985222950\right) a{\left(n + 40 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(56700313723128059710113795527 n^{5} + 11241051880692924547712841309125 n^{4} + 891203143891363204101541081036515 n^{3} + 35318724599102457842244000659066355 n^{2} + 699668074290098868295101668118600758 n + 5542783948087784853117146197416689880\right) a{\left(n + 41 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(83456173136315621774470157429 n^{5} + 15424069120160695811007465359785 n^{4} + 1103923613685761770767490864378825 n^{3} + 38554293209970104773972090050247655 n^{2} + 660343836164158866525694037196135306 n + 4451793809290952082294401827470819720\right) a{\left(n + 33 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(107160812079206688701882214376 n^{5} + 19619093092183955515664225800280 n^{4} + 1435885197652965088921767414927245 n^{3} + 52512736044791763853022341050333550 n^{2} + 959643076333887286644024577578172509 n + 7010366188627064080205343735843425220\right) a{\left(n + 38 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(113340476487510843468918219043 n^{5} + 14573650020324376750669302416225 n^{4} + 668318633029330845796190791211555 n^{3} + 11662567389353045383068448994695495 n^{2} + 9272364941736290378783833339215882 n - 1224686816099384606197066213224410520\right) a{\left(n + 36 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{9 \left(141333028271381937993811773261 n^{5} + 17201843315050550333597347022165 n^{4} + 839293098779568755406793824080865 n^{3} + 20517329245593818915199488299856195 n^{2} + 251270235648482678960697755662144994 n + 1233117267037782310761558487660980120\right) a{\left(n + 25 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{15 \left(210160023586093082689203835683 n^{5} + 29281331257032527318993210792219 n^{4} + 1631606230581321209106486618327243 n^{3} + 45452283541221574920280171719907721 n^{2} + 633044713213760081785682437023918998 n + 3526666118354278204223570857359008208\right) a{\left(n + 29 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(301341785315965934240330877151 n^{5} + 54778148959477941920276064578960 n^{4} + 3976877574109704629271145110236285 n^{3} + 144141892635465490688296595845194820 n^{2} + 2608344666496546639860664350383576184 n + 18852445079582079424015739545030197000\right) a{\left(n + 37 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(421659680385280391421005188109 n^{5} + 62333342855983802148549932852475 n^{4} + 3692023833546944339377354302365845 n^{3} + 109518648430486717573185357894862365 n^{2} + 1626926885297515047253183474964164926 n + 9682000732135574740348456772607181320\right) a{\left(n + 30 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(424955339670930168926136013193 n^{5} + 70123552422201061879525138426390 n^{4} + 4625805110547840989063430174894145 n^{3} + 152485896865480371717522572789614610 n^{2} + 2511877266629727741516648648854078802 n + 16542169300278634730295456893176772400\right) a{\left(n + 35 \right)}}{256 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{5 \left(444947888099083117347087662336 n^{5} + 65599192907249650958534488229971 n^{4} + 3865705152601198865318577621951382 n^{3} + 113817741560313362541886441772779133 n^{2} + 1674337830054829926745498661500852146 n + 9845091953398618236945027964740331656\right) a{\left(n + 31 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(622864787300745772699570589579 n^{5} + 81828658624822474125153497352280 n^{4} + 4301959949182925626090775503268260 n^{3} + 113138517241122141735838281447835055 n^{2} + 1488534823345478445774045378603110196 n + 7838272143509801325000338247607872360\right) a{\left(n + 27 \right)}}{128 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{3 \left(786804455430625864856576135971 n^{5} + 98225734592572928935357306184345 n^{4} + 4901567174985675639595388400872875 n^{3} + 122224152503320760210407311451875055 n^{2} + 1523149324981873934118706864116963154 n + 7589823981533533842727220008623572280\right) a{\left(n + 26 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{3 \left(801556854028467394171913165917 n^{5} + 92384287596150665728546625303735 n^{4} + 4260992956202609435702752004339285 n^{3} + 98322191966431671266877734909591305 n^{2} + 1135234426817193416093840578372531878 n + 5247628997968585680632057477046569400\right) a{\left(n + 24 \right)}}{512 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(2444757122469580022392018669987 n^{5} + 397933881739632725925974230305725 n^{4} + 25886059008196819549996933963606475 n^{3} + 841216249404751424343400123588331635 n^{2} + 13656287547691131798949430496744034338 n + 88598668432369517245079098605756974880\right) a{\left(n + 34 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} - \frac{\left(2608923675906521184772727332043 n^{5} + 343592048447632100548406204583985 n^{4} + 18055146636340492285787907878497915 n^{3} + 473140007621294108199267562538042375 n^{2} + 6182233967087156797850000323469282442 n + 32216972939158600442096141908427040600\right) a{\left(n + 28 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)} + \frac{\left(3950947268585902088537549783681 n^{5} + 600060071952837038416058762154895 n^{4} + 36453635302543070569511692940728345 n^{3} + 1107315092283070784876152409883315665 n^{2} + 16819352866229369368883599677710929494 n + 102204550744546047204730860841050215280\right) a{\left(n + 32 \right)}}{1024 \left(n + 72\right) \left(n + 73\right) \left(n + 74\right) \left(2 n + 145\right) \left(2 n + 147\right)}, \quad n \geq 74\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 74 rules.
Finding the specification took 3865 seconds.
Copy 74 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{0}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{0}\! \left(x \right) F_{20}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{21}\! \left(x \right) F_{24}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{24}\! \left(x \right) &= \frac{F_{25}\! \left(x \right)}{F_{10}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= -F_{10}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= -F_{30}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{35}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{33}\! \left(x \right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{4}\! \left(x \right) F_{50}\! \left(x \right)}\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= -F_{10}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{4}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{49}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= \frac{F_{55}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{55}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{18}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{11}\! \left(x \right) F_{20}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{4}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{10}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{18}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{20}\! \left(x \right) F_{4}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{0}\! \left(x \right) F_{8}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 98 rules.
Finding the specification took 9682 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{7}\! \left(x \right) &= x\\
F_{8}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{7}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{0}\! \left(x \right) F_{10}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{2}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{0}\! \left(x \right) F_{23}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{24}\! \left(x \right) F_{27}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{27}\! \left(x \right) &= \frac{F_{28}\! \left(x \right)}{F_{13}\! \left(x \right) F_{7}\! \left(x \right)}\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= -F_{13}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= -F_{33}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= \frac{F_{32}\! \left(x \right)}{F_{7}\! \left(x \right)}\\
F_{32}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{7}\! \left(x \right)}\\
F_{38}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{36}\! \left(x \right) F_{41}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{7}\! \left(x \right) F_{92}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= -F_{88}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{46}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{7}\! \left(x \right)}\\
F_{48}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{2}\! \left(x \right) F_{51}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{7}\! \left(x \right)}\\
F_{52}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{21}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{21}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{2}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{13}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{21}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{7}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{13}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{41}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{21}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{83}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{23}\! \left(x \right) F_{7}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{0}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{7}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{7}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{92}\! \left(x \right) &= \frac{F_{93}\! \left(x \right)}{F_{7}\! \left(x \right)}\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{11}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{14}\! \left(x \right) F_{23}\! \left(x \right) F_{7}\! \left(x \right)\\
\end{align*}\)