Av(13425, 13452, 14325, 14352, 14532, 41325, 41352, 41532)
Counting Sequence
1, 1, 2, 6, 24, 112, 562, 2918, 15403, 81970, 437954, 2344231, 12557040, 67272371, 360346709, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(81 x^{22}-540 x^{21}+5454 x^{20}-23316 x^{19}+105880 x^{18}-309463 x^{17}+735212 x^{16}-1335670 x^{15}+1530326 x^{14}-1493583 x^{13}+3049706 x^{12}-6766688 x^{11}+9919499 x^{10}-9722923 x^{9}+6690919 x^{8}-3328348 x^{7}+1211881 x^{6}-322925 x^{5}+62202 x^{4}-8423 x^{3}+760 x^{2}-41 x +1\right) F \left(x
\right)^{4}+\left(324 x^{21}-1566 x^{20}+14886 x^{19}-57834 x^{18}+238026 x^{17}-698796 x^{16}+1707853 x^{15}-3794676 x^{14}+7134154 x^{13}-11878642 x^{12}+18112712 x^{11}-23289690 x^{10}+23120582 x^{9}-17029705 x^{8}+9193469 x^{7}-3621970 x^{6}+1035154 x^{5}-211750 x^{4}+30172 x^{3}-2842 x^{2}+159 x -4\right) F \left(x
\right)^{3}+\left(396 x^{20}-1320 x^{19}+12311 x^{18}-39274 x^{17}+171519 x^{16}-543564 x^{15}+1557326 x^{14}-3842021 x^{13}+7419779 x^{12}-11807747 x^{11}+15992004 x^{10}-17580157 x^{9}+14682018 x^{8}-8944843 x^{7}+3911106 x^{6}-1217988 x^{5}+267137 x^{4}-40281 x^{3}+3974 x^{2}-231 x +6\right) F \left(x
\right)^{2}+\left(4 x^{2}-6 x +1\right) \left(36 x^{10}-54 x^{9}+462 x^{8}-1560 x^{7}+2910 x^{6}-4441 x^{5}+4323 x^{4}-2203 x^{3}+584 x^{2}-77 x +4\right) \left(x^{7}+12 x^{5}+9 x^{4}+57 x^{3}-47 x^{2}+12 x -1\right) F \! \left(x \right)+\left(4 x^{2}-6 x +1\right)^{2} \left(x^{7}+12 x^{5}+9 x^{4}+57 x^{3}-47 x^{2}+12 x -1\right)^{2} = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 562\)
\(\displaystyle a(7) = 2918\)
\(\displaystyle a(8) = 15403\)
\(\displaystyle a(9) = 81970\)
\(\displaystyle a(10) = 437954\)
\(\displaystyle a(11) = 2344231\)
\(\displaystyle a(12) = 12557040\)
\(\displaystyle a(13) = 67272371\)
\(\displaystyle a(14) = 360346709\)
\(\displaystyle a(15) = 1929649625\)
\(\displaystyle a(16) = 10329694293\)
\(\displaystyle a(17) = 55277055634\)
\(\displaystyle a(18) = 295705010060\)
\(\displaystyle a(19) = 1581400308694\)
\(\displaystyle a(20) = 8454915181416\)
\(\displaystyle a(21) = 45193513349282\)
\(\displaystyle a(22) = 241522003754139\)
\(\displaystyle a(23) = 1290518212256267\)
\(\displaystyle a(24) = 6894615687395056\)
\(\displaystyle a(25) = 36830250830898821\)
\(\displaystyle a(26) = 196723746050344601\)
\(\displaystyle a(27) = 1050688360790247400\)
\(\displaystyle a(28) = 5611286842633291706\)
\(\displaystyle a(29) = 29965933449296541746\)
\(\displaystyle a(30) = 160020066662270466230\)
\(\displaystyle a(31) = 854488316189165486210\)
\(\displaystyle a(32) = 4562742529221687084660\)
\(\displaystyle a(33) = 24363322260528302099794\)
\(\displaystyle a(34) = 130088789098569096993687\)
\(\displaystyle a(35) = 694604770862955310439579\)
\(\displaystyle a(36) = 3708784289056898285212704\)
\(\displaystyle a(37) = 19802609950411875507847513\)
\(\displaystyle a(38) = 105733166832923449255215563\)
\(\displaystyle a(39) = 564545191893118866846210825\)
\(\displaystyle a(40) = 3014292683051970532437379009\)
\(\displaystyle a(41) = 16094289262788195969867056108\)
\(\displaystyle a(42) = 85932650119280019771056021478\)
\(\displaystyle a(43) = 458822691488908020282510581796\)
\(\displaystyle a(44) = 2449807980724635276340566010776\)
\(\displaystyle a(45) = 13080363617878030275104256089651\)
\(\displaystyle a(46) = 69840654722532747472229293767591\)
\(\displaystyle a(47) = 372904448648614142847949143190823\)
\(\displaystyle a(48) = 1991075102450041109063312865325906\)
\(\displaystyle a(49) = 10631108504075265260924966464701980\)
\(\displaystyle a(50) = 56763647182014352967566359471065077\)
\(\displaystyle a(51) = 303083890993943196022228754499280104\)
\(\displaystyle a(52) = 1618289500220010348212451433067744771\)
\(\displaystyle a(53) = 8640728344492225950100406874853653829\)
\(\displaystyle a(54) = 46136561928142753279647323286056001442\)
\(\displaystyle a(55) = 246343331699449968094614642650324398809\)
\(\displaystyle a(56) = 1315337080410548833413875309190069938468\)
\(\displaystyle a(57) = 7023182412152387061696375667494668150324\)
\(\displaystyle a(58) = 37500013879252723690243616586111028629918\)
\(\displaystyle a(59) = 200230147167441597708883725097660709358774\)
\(\displaystyle a(60) = 1069123871736981124523142485634847591489281\)
\(\displaystyle a(61) = 5708566625755749328928385667093845769692688\)
\(\displaystyle a(62) = 30480815033298991614804684218396727105651169\)
\(\displaystyle a(63) = 162752061793772256543159224062227290961010594\)
\(\displaystyle a(64) = 869014083160225883863750515119882408308345568\)
\(\displaystyle a(65) = 4640101641289385747080216291691990616845242914\)
\(\displaystyle a(66) = 24775846976009164974904108518525551054776839434\)
\(\displaystyle a(67) = 132290859474718066081251700998742666718200655711\)
\(\displaystyle a(68) = 706368712278875804197686377968755088508323452094\)
\(\displaystyle a(69) = 3771666961404435208100875889805253021670121966670\)
\(\displaystyle a(70) = 20138887080743020776018559703718591412714863772937\)
\(\displaystyle a(71) = 107532024783028638626498073325826997326367801728447\)
\(\displaystyle a(72) = 574169858227837175486758827312709621401460145215798\)
\(\displaystyle a(73) = 3065795270561478937225868471927758949234912538687902\)
\(\displaystyle a(74) = 16369902336506918810131085651459595239029877008616609\)
\(\displaystyle a(75) = 87407599135545787016903599942432309240068638759234810\)
\(\displaystyle a(76) = 466715738303045124302166067633870628916704226190732748\)
\(\displaystyle a(77) = 2492044772352148710252820695062657474450485159234135202\)
\(\displaystyle a(78) = 13306362909213254589434537419655264011023883239631259569\)
\(\displaystyle a(79) = 71049823911805544930640391180103864495462868989122836837\)
\(\displaystyle a(80) = 379373295560625807538912747803892297951871056155255557491\)
\(\displaystyle a(81) = 2025678922774512888552417721198258506143168724378976860863\)
\(\displaystyle a{\left(n + 82 \right)} = - \frac{403895160000 \left(n + 1\right) \left(2 n + 5\right) \left(2 n + 7\right) a{\left(n \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{2 \left(86 n + 6715\right) a{\left(n + 81 \right)}}{n + 81} - \frac{\left(14457 n^{2} + 2243175 n + 87011284\right) a{\left(n + 80 \right)}}{\left(n + 80\right) \left(n + 81\right)} + \frac{141717600 \left(2 n + 7\right) \left(278826 n^{2} + 1917250 n + 2711881\right) a{\left(n + 1 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{2 \left(1187096 n^{3} + 274505910 n^{2} + 21158138614 n + 543579636477\right) a{\left(n + 79 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(31726902 n^{3} + 7243905916 n^{2} + 551288672693 n + 13984487375393\right) a{\left(n + 78 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{4723920 \left(350576999 n^{3} + 4625788994 n^{2} + 19688856094 n + 26861403394\right) a{\left(n + 2 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1986202315 n^{3} + 447688600924 n^{2} + 33634962536591 n + 842302941730078\right) a{\left(n + 77 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(25269511240 n^{3} + 5621905464315 n^{2} + 416901841695509 n + 10304994955090918\right) a{\left(n + 76 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{314928 \left(77698226146 n^{3} + 1229843464776 n^{2} + 6376844729861 n + 10794223433496\right) a{\left(n + 3 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1611969781643 n^{3} + 353918345019147 n^{2} + 25900851867996556 n + 631815024704732976\right) a{\left(n + 75 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{78732 \left(3572158890086 n^{3} + 66022916313492 n^{2} + 402763496282311 n + 809446830490717\right) a{\left(n + 4 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(29223716315678 n^{3} + 6330894849532299 n^{2} + 457152150806131234 n + 11003290830134460909\right) a{\left(n + 74 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{4374 \left(611192213987126 n^{3} + 12920040947864502 n^{2} + 90499559062078261 n + 209846403202586607\right) a{\left(n + 5 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(917185180255633 n^{3} + 196016613777963318 n^{2} + 13963553697977370791 n + 331563275516843451894\right) a{\left(n + 73 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(6302940342496109 n^{3} + 1328638297636994214 n^{2} + 93355255484997380668 n + 2186449168780173946731\right) a{\left(n + 72 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{729 \left(29812520893130381 n^{3} + 709810630814935464 n^{2} + 5610298385820787123 n + 14714971309282940460\right) a{\left(n + 6 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(153170758123592719 n^{3} + 31841064070536420060 n^{2} + 2206322152908481178261 n + 50958906942255920965992\right) a{\left(n + 71 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{729 \left(423471619613912009 n^{3} + 11218255122821175242 n^{2} + 98734275882971144935 n + 288701635267882449918\right) a{\left(n + 7 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(3315695637812237203 n^{3} + 679600927375054410828 n^{2} + 46430580031866876999185 n + 1057365867130436102517240\right) a{\left(n + 70 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(16082640696857042936 n^{3} + 3249547543572391119861 n^{2} + 218857007733428329155859 n + 4913265560257858615875228\right) a{\left(n + 69 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{81 \left(24003721055122305863 n^{3} + 700513428477108895536 n^{2} + 6793577454604954484683 n + 21899394540950772170838\right) a{\left(n + 8 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(140545053617753151529 n^{3} + 27988868364901703801475 n^{2} + 1857925515512158289635847 n + 41109731189386669396400397\right) a{\left(n + 68 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{27 \left(406370501146335770603 n^{3} + 12957067872577567658914 n^{2} + 137282081080186177152169 n + 483528905098352738916794\right) a{\left(n + 9 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(740701369086677635681 n^{3} + 145356602934499151024830 n^{2} + 9508252101639787122511905 n + 207319954451921018041500952\right) a{\left(n + 67 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{9 \left(3105460762345048096476 n^{3} + 107425290240246956092364 n^{2} + 1234597183807518144050463 n + 4716330251836149026957269\right) a{\left(n + 10 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(15945477311703672921901 n^{3} + 3082964105939327297382696 n^{2} + 198689437379131091776767857 n + 4268316684242164573923104994\right) a{\left(n + 66 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(104156065366802972993395 n^{3} + 19836842684493587530482186 n^{2} + 1259322239147613665036913989 n + 26648802165587938753968266670\right) a{\left(n + 65 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{3 \left(172320641244373364058177 n^{3} + 6427900477737497457871910 n^{2} + 79638967277547020528580903 n + 327906462338935536084226666\right) a{\left(n + 11 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(206901855787934610514557 n^{3} + 38808583572105480146360440 n^{2} + 2426433442679558433295029687 n + 50569223718527858844069389820\right) a{\left(n + 64 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(1088825724912559699779695 n^{3} + 43561120577709788213274603 n^{2} + 578682958901617982545402732 n + 2554058559230855735873047950\right) a{\left(n + 12 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(3380692802466440215528679 n^{3} + 624401825757223631081054922 n^{2} + 38441512317498118428067445371 n + 788886821991342958093660455084\right) a{\left(n + 63 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(8374756678678072743086077 n^{3} + 357601413327000483030912116 n^{2} + 5068803701205756522322467695 n + 23863190925514368143413185016\right) a{\left(n + 13 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(8425206547925639960304686 n^{3} + 1531989138621588264003907176 n^{2} + 92855805114143121518158178365 n + 1876034065721753255186063899725\right) a{\left(n + 62 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(14714783669242085262715217 n^{3} + 667568756730896037050181368 n^{2} + 10050897351579940025464746369 n + 50245273212201573655825065410\right) a{\left(n + 14 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(76926359920025582639517151 n^{3} + 13768658574269269469839670664 n^{2} + 821459867020179268024832526767 n + 16336511580123956028896015744178\right) a{\left(n + 61 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(94456153825423344641710723 n^{3} + 4533152332521091948789834938 n^{2} + 72183475896890119051617200977 n + 381524382545652068862149920938\right) a{\left(n + 15 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(138193245436656022167213333 n^{3} + 6985598505188369822880949877 n^{2} + 117139176940313957389931344814 n + 651798837297291964928349738324\right) a{\left(n + 16 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(308366033167335343024589591 n^{3} + 53451423098225195843564006946 n^{2} + 3088364396343971929791331665880 n + 59480438361170695482401948905191\right) a{\left(n + 59 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(321798990321296570989457245 n^{3} + 56685439453304505247133811846 n^{2} + 3328404740125417702521254681303 n + 65144601432550636410983759760558\right) a{\left(n + 60 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(734779451951671158462502711 n^{3} + 38943566039311203606629748688 n^{2} + 684571701262092416051473190213 n + 3991842464067579121380976005788\right) a{\left(n + 17 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(1323914521049525975575301776 n^{3} + 73186552150323394064638042536 n^{2} + 1341591440631128005949371084157 n + 8154677872705460715500480538267\right) a{\left(n + 18 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(2850804579972188471628361268 n^{3} + 163282344025250614817641847658 n^{2} + 3100098964418064054620681812003 n + 19504315574431749151704487557165\right) a{\left(n + 19 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(2896995017906206252299296130 n^{3} - 343489994778188390924917055143 n^{2} - 20842743707011922696952650931347 n - 260690145701652966744289054216488\right) a{\left(n + 25 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(4329844799808913868110813919 n^{3} + 738441026828569960674599833680 n^{2} + 41979137364502851011205672296905 n + 795472472997659804535821680900536\right) a{\left(n + 58 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(4634720109473806034009340901 n^{3} + 777635939857731159218565892246 n^{2} + 43491005947589960965171417896549 n + 810760481516315944253432866354856\right) a{\left(n + 57 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(7247222552349986565393207379 n^{3} + 425907696296638003908617213370 n^{2} + 8289247397838179760784439485765 n + 53383602737263776282398741764870\right) a{\left(n + 20 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(8391059088562891240578067378 n^{3} - 1438926022504876622086848190065 n^{2} - 79588934278930067710500139000516 n - 946673328685323797038307914260477\right) a{\left(n + 26 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(14396147713283826139341161425 n^{3} + 355164975376210731443618364690 n^{2} - 6654773891720125216311131463489 n - 164920939980837525701262372327562\right) a{\left(n + 24 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(20386015717506941494195943893 n^{3} + 3364911010609884252329570916114 n^{2} + 185130899517271376133090009151946 n + 3395064018388268246585527273566303\right) a{\left(n + 56 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(25548027755358540863740353904 n^{3} + 30632350149991244697236714896713 n^{2} + 2668914162965541949521288492733541 n + 60444034147871467449133358020088574\right) a{\left(n + 47 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(36014580661124589800962525421 n^{3} + 2135505473337184537684202691972 n^{2} + 41800562451407588407912604356201 n + 269523761251906121417922519191622\right) a{\left(n + 21 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(50224999938974819279694901351 n^{3} + 2899796741655322453795052153982 n^{2} + 54503587532967228937752645400535 n + 330374964640632256759724303901300\right) a{\left(n + 22 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(55641816030447403110488949887 n^{3} + 2824682219680220797548107746104 n^{2} + 42299754201850901494502363630785 n + 155925858945156047797507164749040\right) a{\left(n + 23 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(62104203543975898474319896889 n^{3} + 3719492780362250122879717528473 n^{2} + 88393315170398268641926708030654 n + 901210099294825100116143382340700\right) a{\left(n + 27 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(108880017037838702319257591251 n^{3} + 17680251003971652554340466308660 n^{2} + 956936190769700265399536282613551 n + 17263605623691015102097290386732826\right) a{\left(n + 55 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(222099592884156307950059573174 n^{3} + 20849135186919303578297853084621 n^{2} + 682317311976714212678342700552418 n + 7639112562063703014322498000510599\right) a{\left(n + 28 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(263739959886277599197756460383 n^{3} + 42138201095852442920367796668594 n^{2} + 2243958594696662432099854608398857 n + 39828354753999535428684329853640518\right) a{\left(n + 54 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(350820338698897698578619858897 n^{3} + 37204595640942033797343492272940 n^{2} + 1304870181779514657111689704947421 n + 15110842152671854703959737631749838\right) a{\left(n + 29 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(576099749615410279337146938047 n^{3} + 90594612252483662582073724070412 n^{2} + 4748108285335752100024294496599489 n + 82937882726481380501139933787332924\right) a{\left(n + 53 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(967009329807494484788734098632 n^{3} + 147716343814678957686242626654290 n^{2} + 7518246302934403874135424145236409 n + 127497305131387274479844691485160969\right) a{\left(n + 51 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(993291518049651190499950185929 n^{3} + 111981852967228710914183382420642 n^{2} + 4083822626987204407858106477998510 n + 48551268609525237187481960082564495\right) a{\left(n + 30 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(1124676906340852409846799017897 n^{3} + 174193739140460769367156501937538 n^{2} + 8990994243250990699702607823865597 n + 154651969115579282403641848955789424\right) a{\left(n + 52 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{2 \left(1498134425520806623942692242408 n^{3} + 190754735142566953406515426586688 n^{2} + 8070447366658427089220786269044286 n + 113408099027823923158830429613727955\right) a{\left(n + 45 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1693273282488146319054361021681 n^{3} + 194742828021963580662532198872168 n^{2} + 7214393056239009200394846531661292 n + 86940661819627061422778664685429383\right) a{\left(n + 31 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1736558236533300322927778936161 n^{3} + 213013909821337732816916685771250 n^{2} + 8600846348512538661647652260779719 n + 113919267840221666221089622060250374\right) a{\left(n + 46 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(2794640083020662502053649186467 n^{3} + 431755443411702099328252376474412 n^{2} + 22071850181903537786484656026532017 n + 373779468381958109167671761649545928\right) a{\left(n + 48 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(2853943166473652806517363765683 n^{3} + 431230696563459072684233974707660 n^{2} + 21701605218907632990464377294742711 n + 363756435557815005946448375718922842\right) a{\left(n + 50 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(3416547217004269004504632479853 n^{3} + 514482569148370300845314230026894 n^{2} + 25774717648103112599775764449670243 n + 429660974370990175391551354490956746\right) a{\left(n + 49 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(3593950091265193077871447568163 n^{3} + 367964668396402170998734453211536 n^{2} + 12497255759548666439219523279100059 n + 140696367706211029942956523943056896\right) a{\left(n + 36 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(4566248011347113045030597380118 n^{3} + 640947300901917041387126645919594 n^{2} + 29414368067877867570844245497059543 n + 443178931271932239967645734580987041\right) a{\left(n + 42 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(5158158439589133572206235453060 n^{3} + 552865493207060072519720946020883 n^{2} + 19533564499241082189950123692375948 n + 227901883063163517898258914578298957\right) a{\left(n + 33 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(5790414274788357193953122437789 n^{3} + 650315571601712340785094015226086 n^{2} + 23769630851858662875606148196428397 n + 284436629489472923024302278489334776\right) a{\left(n + 32 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(5808126714654278917915125500603 n^{3} + 743464736330267891717474950225600 n^{2} + 31658857924471665086864835774714353 n + 448416642880604417814531031406814132\right) a{\left(n + 44 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{2 \left(6672265421074648937015529965183 n^{3} + 691452982792260202804307258252835 n^{2} + 23761407133590144956945899759295383 n + 270533991558933880754631188503568964\right) a{\left(n + 37 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(7655203900115914646474527406491 n^{3} + 654035489295274408498844869645152 n^{2} + 15718316580422951030720245013669291 n + 72362110211188970718507473738396778\right) a{\left(n + 41 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(7741367317458531299878975848583 n^{3} + 821185529243180148928440866234199 n^{2} + 28825785349946662426546562419112258 n + 334355610615725356648283281482586268\right) a{\left(n + 39 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(9128227277755756279617237446687 n^{3} + 943664886752371318967427184696665 n^{2} + 32343473439809817787236236153011318 n + 367575849574598534736912347214920106\right) a{\left(n + 34 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(9962228114858019857160096239137 n^{3} + 1016244258621031413715236765457348 n^{2} + 34399395964690573942483605872776831 n + 386209068079626060782612349621732076\right) a{\left(n + 35 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(14254592339082593726737572569348 n^{3} + 1496069890184425565331595488533379 n^{2} + 51626652634338957367898284147785346 n + 583515182104364957842592016051354267\right) a{\left(n + 40 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(17522650379849377782719663197061 n^{3} + 2264764790771331297643937623723170 n^{2} + 97275816849931001827087852663488865 n + 1388607116148799458356123286527404344\right) a{\left(n + 43 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(55396553929878968116975389186283 n^{3} + 5821429037467354126693628757427830 n^{2} + 202749975263373010050086322325962557 n + 2337927639429702219452304518353140234\right) a{\left(n + 38 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)}, \quad n \geq 82\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 562\)
\(\displaystyle a(7) = 2918\)
\(\displaystyle a(8) = 15403\)
\(\displaystyle a(9) = 81970\)
\(\displaystyle a(10) = 437954\)
\(\displaystyle a(11) = 2344231\)
\(\displaystyle a(12) = 12557040\)
\(\displaystyle a(13) = 67272371\)
\(\displaystyle a(14) = 360346709\)
\(\displaystyle a(15) = 1929649625\)
\(\displaystyle a(16) = 10329694293\)
\(\displaystyle a(17) = 55277055634\)
\(\displaystyle a(18) = 295705010060\)
\(\displaystyle a(19) = 1581400308694\)
\(\displaystyle a(20) = 8454915181416\)
\(\displaystyle a(21) = 45193513349282\)
\(\displaystyle a(22) = 241522003754139\)
\(\displaystyle a(23) = 1290518212256267\)
\(\displaystyle a(24) = 6894615687395056\)
\(\displaystyle a(25) = 36830250830898821\)
\(\displaystyle a(26) = 196723746050344601\)
\(\displaystyle a(27) = 1050688360790247400\)
\(\displaystyle a(28) = 5611286842633291706\)
\(\displaystyle a(29) = 29965933449296541746\)
\(\displaystyle a(30) = 160020066662270466230\)
\(\displaystyle a(31) = 854488316189165486210\)
\(\displaystyle a(32) = 4562742529221687084660\)
\(\displaystyle a(33) = 24363322260528302099794\)
\(\displaystyle a(34) = 130088789098569096993687\)
\(\displaystyle a(35) = 694604770862955310439579\)
\(\displaystyle a(36) = 3708784289056898285212704\)
\(\displaystyle a(37) = 19802609950411875507847513\)
\(\displaystyle a(38) = 105733166832923449255215563\)
\(\displaystyle a(39) = 564545191893118866846210825\)
\(\displaystyle a(40) = 3014292683051970532437379009\)
\(\displaystyle a(41) = 16094289262788195969867056108\)
\(\displaystyle a(42) = 85932650119280019771056021478\)
\(\displaystyle a(43) = 458822691488908020282510581796\)
\(\displaystyle a(44) = 2449807980724635276340566010776\)
\(\displaystyle a(45) = 13080363617878030275104256089651\)
\(\displaystyle a(46) = 69840654722532747472229293767591\)
\(\displaystyle a(47) = 372904448648614142847949143190823\)
\(\displaystyle a(48) = 1991075102450041109063312865325906\)
\(\displaystyle a(49) = 10631108504075265260924966464701980\)
\(\displaystyle a(50) = 56763647182014352967566359471065077\)
\(\displaystyle a(51) = 303083890993943196022228754499280104\)
\(\displaystyle a(52) = 1618289500220010348212451433067744771\)
\(\displaystyle a(53) = 8640728344492225950100406874853653829\)
\(\displaystyle a(54) = 46136561928142753279647323286056001442\)
\(\displaystyle a(55) = 246343331699449968094614642650324398809\)
\(\displaystyle a(56) = 1315337080410548833413875309190069938468\)
\(\displaystyle a(57) = 7023182412152387061696375667494668150324\)
\(\displaystyle a(58) = 37500013879252723690243616586111028629918\)
\(\displaystyle a(59) = 200230147167441597708883725097660709358774\)
\(\displaystyle a(60) = 1069123871736981124523142485634847591489281\)
\(\displaystyle a(61) = 5708566625755749328928385667093845769692688\)
\(\displaystyle a(62) = 30480815033298991614804684218396727105651169\)
\(\displaystyle a(63) = 162752061793772256543159224062227290961010594\)
\(\displaystyle a(64) = 869014083160225883863750515119882408308345568\)
\(\displaystyle a(65) = 4640101641289385747080216291691990616845242914\)
\(\displaystyle a(66) = 24775846976009164974904108518525551054776839434\)
\(\displaystyle a(67) = 132290859474718066081251700998742666718200655711\)
\(\displaystyle a(68) = 706368712278875804197686377968755088508323452094\)
\(\displaystyle a(69) = 3771666961404435208100875889805253021670121966670\)
\(\displaystyle a(70) = 20138887080743020776018559703718591412714863772937\)
\(\displaystyle a(71) = 107532024783028638626498073325826997326367801728447\)
\(\displaystyle a(72) = 574169858227837175486758827312709621401460145215798\)
\(\displaystyle a(73) = 3065795270561478937225868471927758949234912538687902\)
\(\displaystyle a(74) = 16369902336506918810131085651459595239029877008616609\)
\(\displaystyle a(75) = 87407599135545787016903599942432309240068638759234810\)
\(\displaystyle a(76) = 466715738303045124302166067633870628916704226190732748\)
\(\displaystyle a(77) = 2492044772352148710252820695062657474450485159234135202\)
\(\displaystyle a(78) = 13306362909213254589434537419655264011023883239631259569\)
\(\displaystyle a(79) = 71049823911805544930640391180103864495462868989122836837\)
\(\displaystyle a(80) = 379373295560625807538912747803892297951871056155255557491\)
\(\displaystyle a(81) = 2025678922774512888552417721198258506143168724378976860863\)
\(\displaystyle a{\left(n + 82 \right)} = - \frac{403895160000 \left(n + 1\right) \left(2 n + 5\right) \left(2 n + 7\right) a{\left(n \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{2 \left(86 n + 6715\right) a{\left(n + 81 \right)}}{n + 81} - \frac{\left(14457 n^{2} + 2243175 n + 87011284\right) a{\left(n + 80 \right)}}{\left(n + 80\right) \left(n + 81\right)} + \frac{141717600 \left(2 n + 7\right) \left(278826 n^{2} + 1917250 n + 2711881\right) a{\left(n + 1 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{2 \left(1187096 n^{3} + 274505910 n^{2} + 21158138614 n + 543579636477\right) a{\left(n + 79 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(31726902 n^{3} + 7243905916 n^{2} + 551288672693 n + 13984487375393\right) a{\left(n + 78 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{4723920 \left(350576999 n^{3} + 4625788994 n^{2} + 19688856094 n + 26861403394\right) a{\left(n + 2 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1986202315 n^{3} + 447688600924 n^{2} + 33634962536591 n + 842302941730078\right) a{\left(n + 77 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(25269511240 n^{3} + 5621905464315 n^{2} + 416901841695509 n + 10304994955090918\right) a{\left(n + 76 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{314928 \left(77698226146 n^{3} + 1229843464776 n^{2} + 6376844729861 n + 10794223433496\right) a{\left(n + 3 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1611969781643 n^{3} + 353918345019147 n^{2} + 25900851867996556 n + 631815024704732976\right) a{\left(n + 75 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{78732 \left(3572158890086 n^{3} + 66022916313492 n^{2} + 402763496282311 n + 809446830490717\right) a{\left(n + 4 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(29223716315678 n^{3} + 6330894849532299 n^{2} + 457152150806131234 n + 11003290830134460909\right) a{\left(n + 74 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{4374 \left(611192213987126 n^{3} + 12920040947864502 n^{2} + 90499559062078261 n + 209846403202586607\right) a{\left(n + 5 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(917185180255633 n^{3} + 196016613777963318 n^{2} + 13963553697977370791 n + 331563275516843451894\right) a{\left(n + 73 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(6302940342496109 n^{3} + 1328638297636994214 n^{2} + 93355255484997380668 n + 2186449168780173946731\right) a{\left(n + 72 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{729 \left(29812520893130381 n^{3} + 709810630814935464 n^{2} + 5610298385820787123 n + 14714971309282940460\right) a{\left(n + 6 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(153170758123592719 n^{3} + 31841064070536420060 n^{2} + 2206322152908481178261 n + 50958906942255920965992\right) a{\left(n + 71 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{729 \left(423471619613912009 n^{3} + 11218255122821175242 n^{2} + 98734275882971144935 n + 288701635267882449918\right) a{\left(n + 7 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(3315695637812237203 n^{3} + 679600927375054410828 n^{2} + 46430580031866876999185 n + 1057365867130436102517240\right) a{\left(n + 70 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(16082640696857042936 n^{3} + 3249547543572391119861 n^{2} + 218857007733428329155859 n + 4913265560257858615875228\right) a{\left(n + 69 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{81 \left(24003721055122305863 n^{3} + 700513428477108895536 n^{2} + 6793577454604954484683 n + 21899394540950772170838\right) a{\left(n + 8 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(140545053617753151529 n^{3} + 27988868364901703801475 n^{2} + 1857925515512158289635847 n + 41109731189386669396400397\right) a{\left(n + 68 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{27 \left(406370501146335770603 n^{3} + 12957067872577567658914 n^{2} + 137282081080186177152169 n + 483528905098352738916794\right) a{\left(n + 9 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(740701369086677635681 n^{3} + 145356602934499151024830 n^{2} + 9508252101639787122511905 n + 207319954451921018041500952\right) a{\left(n + 67 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{9 \left(3105460762345048096476 n^{3} + 107425290240246956092364 n^{2} + 1234597183807518144050463 n + 4716330251836149026957269\right) a{\left(n + 10 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(15945477311703672921901 n^{3} + 3082964105939327297382696 n^{2} + 198689437379131091776767857 n + 4268316684242164573923104994\right) a{\left(n + 66 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(104156065366802972993395 n^{3} + 19836842684493587530482186 n^{2} + 1259322239147613665036913989 n + 26648802165587938753968266670\right) a{\left(n + 65 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{3 \left(172320641244373364058177 n^{3} + 6427900477737497457871910 n^{2} + 79638967277547020528580903 n + 327906462338935536084226666\right) a{\left(n + 11 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(206901855787934610514557 n^{3} + 38808583572105480146360440 n^{2} + 2426433442679558433295029687 n + 50569223718527858844069389820\right) a{\left(n + 64 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(1088825724912559699779695 n^{3} + 43561120577709788213274603 n^{2} + 578682958901617982545402732 n + 2554058559230855735873047950\right) a{\left(n + 12 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(3380692802466440215528679 n^{3} + 624401825757223631081054922 n^{2} + 38441512317498118428067445371 n + 788886821991342958093660455084\right) a{\left(n + 63 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(8374756678678072743086077 n^{3} + 357601413327000483030912116 n^{2} + 5068803701205756522322467695 n + 23863190925514368143413185016\right) a{\left(n + 13 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(8425206547925639960304686 n^{3} + 1531989138621588264003907176 n^{2} + 92855805114143121518158178365 n + 1876034065721753255186063899725\right) a{\left(n + 62 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(14714783669242085262715217 n^{3} + 667568756730896037050181368 n^{2} + 10050897351579940025464746369 n + 50245273212201573655825065410\right) a{\left(n + 14 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(76926359920025582639517151 n^{3} + 13768658574269269469839670664 n^{2} + 821459867020179268024832526767 n + 16336511580123956028896015744178\right) a{\left(n + 61 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(94456153825423344641710723 n^{3} + 4533152332521091948789834938 n^{2} + 72183475896890119051617200977 n + 381524382545652068862149920938\right) a{\left(n + 15 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(138193245436656022167213333 n^{3} + 6985598505188369822880949877 n^{2} + 117139176940313957389931344814 n + 651798837297291964928349738324\right) a{\left(n + 16 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(308366033167335343024589591 n^{3} + 53451423098225195843564006946 n^{2} + 3088364396343971929791331665880 n + 59480438361170695482401948905191\right) a{\left(n + 59 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(321798990321296570989457245 n^{3} + 56685439453304505247133811846 n^{2} + 3328404740125417702521254681303 n + 65144601432550636410983759760558\right) a{\left(n + 60 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(734779451951671158462502711 n^{3} + 38943566039311203606629748688 n^{2} + 684571701262092416051473190213 n + 3991842464067579121380976005788\right) a{\left(n + 17 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(1323914521049525975575301776 n^{3} + 73186552150323394064638042536 n^{2} + 1341591440631128005949371084157 n + 8154677872705460715500480538267\right) a{\left(n + 18 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(2850804579972188471628361268 n^{3} + 163282344025250614817641847658 n^{2} + 3100098964418064054620681812003 n + 19504315574431749151704487557165\right) a{\left(n + 19 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(2896995017906206252299296130 n^{3} - 343489994778188390924917055143 n^{2} - 20842743707011922696952650931347 n - 260690145701652966744289054216488\right) a{\left(n + 25 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(4329844799808913868110813919 n^{3} + 738441026828569960674599833680 n^{2} + 41979137364502851011205672296905 n + 795472472997659804535821680900536\right) a{\left(n + 58 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(4634720109473806034009340901 n^{3} + 777635939857731159218565892246 n^{2} + 43491005947589960965171417896549 n + 810760481516315944253432866354856\right) a{\left(n + 57 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(7247222552349986565393207379 n^{3} + 425907696296638003908617213370 n^{2} + 8289247397838179760784439485765 n + 53383602737263776282398741764870\right) a{\left(n + 20 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(8391059088562891240578067378 n^{3} - 1438926022504876622086848190065 n^{2} - 79588934278930067710500139000516 n - 946673328685323797038307914260477\right) a{\left(n + 26 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(14396147713283826139341161425 n^{3} + 355164975376210731443618364690 n^{2} - 6654773891720125216311131463489 n - 164920939980837525701262372327562\right) a{\left(n + 24 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(20386015717506941494195943893 n^{3} + 3364911010609884252329570916114 n^{2} + 185130899517271376133090009151946 n + 3395064018388268246585527273566303\right) a{\left(n + 56 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(25548027755358540863740353904 n^{3} + 30632350149991244697236714896713 n^{2} + 2668914162965541949521288492733541 n + 60444034147871467449133358020088574\right) a{\left(n + 47 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(36014580661124589800962525421 n^{3} + 2135505473337184537684202691972 n^{2} + 41800562451407588407912604356201 n + 269523761251906121417922519191622\right) a{\left(n + 21 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(50224999938974819279694901351 n^{3} + 2899796741655322453795052153982 n^{2} + 54503587532967228937752645400535 n + 330374964640632256759724303901300\right) a{\left(n + 22 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(55641816030447403110488949887 n^{3} + 2824682219680220797548107746104 n^{2} + 42299754201850901494502363630785 n + 155925858945156047797507164749040\right) a{\left(n + 23 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(62104203543975898474319896889 n^{3} + 3719492780362250122879717528473 n^{2} + 88393315170398268641926708030654 n + 901210099294825100116143382340700\right) a{\left(n + 27 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(108880017037838702319257591251 n^{3} + 17680251003971652554340466308660 n^{2} + 956936190769700265399536282613551 n + 17263605623691015102097290386732826\right) a{\left(n + 55 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(222099592884156307950059573174 n^{3} + 20849135186919303578297853084621 n^{2} + 682317311976714212678342700552418 n + 7639112562063703014322498000510599\right) a{\left(n + 28 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(263739959886277599197756460383 n^{3} + 42138201095852442920367796668594 n^{2} + 2243958594696662432099854608398857 n + 39828354753999535428684329853640518\right) a{\left(n + 54 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(350820338698897698578619858897 n^{3} + 37204595640942033797343492272940 n^{2} + 1304870181779514657111689704947421 n + 15110842152671854703959737631749838\right) a{\left(n + 29 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(576099749615410279337146938047 n^{3} + 90594612252483662582073724070412 n^{2} + 4748108285335752100024294496599489 n + 82937882726481380501139933787332924\right) a{\left(n + 53 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(967009329807494484788734098632 n^{3} + 147716343814678957686242626654290 n^{2} + 7518246302934403874135424145236409 n + 127497305131387274479844691485160969\right) a{\left(n + 51 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(993291518049651190499950185929 n^{3} + 111981852967228710914183382420642 n^{2} + 4083822626987204407858106477998510 n + 48551268609525237187481960082564495\right) a{\left(n + 30 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(1124676906340852409846799017897 n^{3} + 174193739140460769367156501937538 n^{2} + 8990994243250990699702607823865597 n + 154651969115579282403641848955789424\right) a{\left(n + 52 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{2 \left(1498134425520806623942692242408 n^{3} + 190754735142566953406515426586688 n^{2} + 8070447366658427089220786269044286 n + 113408099027823923158830429613727955\right) a{\left(n + 45 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1693273282488146319054361021681 n^{3} + 194742828021963580662532198872168 n^{2} + 7214393056239009200394846531661292 n + 86940661819627061422778664685429383\right) a{\left(n + 31 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(1736558236533300322927778936161 n^{3} + 213013909821337732816916685771250 n^{2} + 8600846348512538661647652260779719 n + 113919267840221666221089622060250374\right) a{\left(n + 46 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(2794640083020662502053649186467 n^{3} + 431755443411702099328252376474412 n^{2} + 22071850181903537786484656026532017 n + 373779468381958109167671761649545928\right) a{\left(n + 48 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(2853943166473652806517363765683 n^{3} + 431230696563459072684233974707660 n^{2} + 21701605218907632990464377294742711 n + 363756435557815005946448375718922842\right) a{\left(n + 50 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(3416547217004269004504632479853 n^{3} + 514482569148370300845314230026894 n^{2} + 25774717648103112599775764449670243 n + 429660974370990175391551354490956746\right) a{\left(n + 49 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(3593950091265193077871447568163 n^{3} + 367964668396402170998734453211536 n^{2} + 12497255759548666439219523279100059 n + 140696367706211029942956523943056896\right) a{\left(n + 36 \right)}}{\left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(4566248011347113045030597380118 n^{3} + 640947300901917041387126645919594 n^{2} + 29414368067877867570844245497059543 n + 443178931271932239967645734580987041\right) a{\left(n + 42 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(5158158439589133572206235453060 n^{3} + 552865493207060072519720946020883 n^{2} + 19533564499241082189950123692375948 n + 227901883063163517898258914578298957\right) a{\left(n + 33 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(5790414274788357193953122437789 n^{3} + 650315571601712340785094015226086 n^{2} + 23769630851858662875606148196428397 n + 284436629489472923024302278489334776\right) a{\left(n + 32 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(5808126714654278917915125500603 n^{3} + 743464736330267891717474950225600 n^{2} + 31658857924471665086864835774714353 n + 448416642880604417814531031406814132\right) a{\left(n + 44 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{2 \left(6672265421074648937015529965183 n^{3} + 691452982792260202804307258252835 n^{2} + 23761407133590144956945899759295383 n + 270533991558933880754631188503568964\right) a{\left(n + 37 \right)}}{3 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(7655203900115914646474527406491 n^{3} + 654035489295274408498844869645152 n^{2} + 15718316580422951030720245013669291 n + 72362110211188970718507473738396778\right) a{\left(n + 41 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(7741367317458531299878975848583 n^{3} + 821185529243180148928440866234199 n^{2} + 28825785349946662426546562419112258 n + 334355610615725356648283281482586268\right) a{\left(n + 39 \right)}}{2 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(9128227277755756279617237446687 n^{3} + 943664886752371318967427184696665 n^{2} + 32343473439809817787236236153011318 n + 367575849574598534736912347214920106\right) a{\left(n + 34 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} + \frac{\left(9962228114858019857160096239137 n^{3} + 1016244258621031413715236765457348 n^{2} + 34399395964690573942483605872776831 n + 386209068079626060782612349621732076\right) a{\left(n + 35 \right)}}{4 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(14254592339082593726737572569348 n^{3} + 1496069890184425565331595488533379 n^{2} + 51626652634338957367898284147785346 n + 583515182104364957842592016051354267\right) a{\left(n + 40 \right)}}{6 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(17522650379849377782719663197061 n^{3} + 2264764790771331297643937623723170 n^{2} + 97275816849931001827087852663488865 n + 1388607116148799458356123286527404344\right) a{\left(n + 43 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)} - \frac{\left(55396553929878968116975389186283 n^{3} + 5821429037467354126693628757427830 n^{2} + 202749975263373010050086322325962557 n + 2337927639429702219452304518353140234\right) a{\left(n + 38 \right)}}{12 \left(n + 79\right) \left(n + 80\right) \left(n + 81\right)}, \quad n \geq 82\)
This specification was found using the strategy pack "Point And Row And Col Placements Req Corrob" and has 249 rules.
Finding the specification took 52995 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_{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_{134}\! \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_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{21}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{35}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{34}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{40}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{37}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{39}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{34}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{4}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{51}\! \left(x \right) &= 0\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{4}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{4}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{62}\! \left(x \right)+F_{64}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{25} \left(x \right)^{2}\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{25}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{66}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{4}\! \left(x \right) F_{77}\! \left(x \right)}\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{4}\! \left(x \right) F_{71}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{77}\! \left(x \right) &= \frac{F_{78}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{78}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{4}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{4}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= \frac{F_{87}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{87}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{37}\! \left(x \right) F_{4}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{80}\! \left(x \right)+F_{94}\! \left(x \right)+F_{95}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{4}\! \left(x \right) F_{60}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{25}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{4}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{103}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{25}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{107}\! \left(x \right)+F_{109}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{4}\! \left(x \right) F_{71}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{103}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{4}\! \left(x \right) F_{72}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{4}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{20}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{119}\! \left(x \right) &= \frac{F_{120}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{129}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{13}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= -F_{243}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{158}\! \left(x \right)+F_{160}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{142}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{151}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{156}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{140}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)+F_{216}\! \left(x \right)+F_{242}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{192}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{190}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{166}\! \left(x \right) &= \frac{F_{167}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{167}\! \left(x \right) &= -F_{168}\! \left(x \right)-F_{184}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{173}\! \left(x \right) F_{181}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{178}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{188}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{37}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{128}\! \left(x \right) F_{173}\! \left(x \right) F_{4}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{186}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{128}\! \left(x \right) F_{25}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{198}\! \left(x \right)+F_{214}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{196}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{188}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{201}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{203}\! \left(x \right) &= \frac{F_{204}\! \left(x \right)}{F_{24}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= -F_{206}\! \left(x \right)-F_{207}\! \left(x \right)-F_{209}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{181}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{17}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{206}\! \left(x \right)+F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{211}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{211}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{218}\! \left(x \right) &= \frac{F_{219}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{224}\! \left(x \right)+F_{226}\! \left(x \right)+F_{235}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{24} \left(x \right)^{2} F_{181}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{222}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{211}\! \left(x \right) F_{228}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)+F_{230}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{24}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{233}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{228}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{230}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{24} \left(x \right)^{2} F_{203}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{222}\! \left(x \right) F_{239}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{239}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{161}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{244}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{128}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{246}\! \left(x \right) &= -F_{247}\! \left(x \right)+F_{222}\! \left(x \right)\\
F_{247}\! \left(x \right) &= \frac{F_{248}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{248}\! \left(x \right) &= F_{19}\! \left(x \right)\\
\end{align*}\)