Av(12354, 13254, 13524, 13542, 31254, 31524, 31542, 35124, 35142)
Counting Sequence
1, 1, 2, 6, 24, 111, 546, 2760, 14152, 73217, 381242, 1995171, 10485030, 55297740, 292550930, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(5 x -1\right) \left(x -1\right)^{3} x^{2} F \left(x
\right)^{6}+2 x \left(5 x -1\right) \left(x^{2}-x +1\right) \left(x -1\right)^{2} F \left(x
\right)^{5}+\left(-11 x^{6}+52 x^{5}-90 x^{4}+66 x^{3}-15 x^{2}-4 x +1\right) F \left(x
\right)^{4}-\left(x -1\right) \left(5 x -1\right) \left(x^{3}+4 x^{2}-8 x +4\right) F \left(x
\right)^{3}-\left(x -1\right) \left(5 x -1\right) \left(x^{3}-12 x^{2}+16 x -6\right) F \left(x
\right)^{2}-2 \left(5 x -1\right) \left(3 x -2\right) \left(x -1\right)^{2} F \! \left(x \right)+\left(5 x -1\right) \left(x -1\right)^{3} = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 111\)
\(\displaystyle a(6) = 546\)
\(\displaystyle a(7) = 2760\)
\(\displaystyle a(8) = 14152\)
\(\displaystyle a(9) = 73217\)
\(\displaystyle a(10) = 381242\)
\(\displaystyle a(11) = 1995171\)
\(\displaystyle a(12) = 10485030\)
\(\displaystyle a(13) = 55297740\)
\(\displaystyle a(14) = 292550930\)
\(\displaystyle a(15) = 1552049418\)
\(\displaystyle a(16) = 8254753736\)
\(\displaystyle a(17) = 44005185216\)
\(\displaystyle a(18) = 235086465558\)
\(\displaystyle a(19) = 1258376412334\)
\(\displaystyle a(20) = 6748344118162\)
\(\displaystyle a(21) = 36252626922701\)
\(\displaystyle a(22) = 195072072628438\)
\(\displaystyle a(23) = 1051299650526297\)
\(\displaystyle a(24) = 5674139791228478\)
\(\displaystyle a(25) = 30667973501678763\)
\(\displaystyle a(26) = 165979232714361346\)
\(\displaystyle a(27) = 899456918761173937\)
\(\displaystyle a(28) = 4880239532203966838\)
\(\displaystyle a(29) = 26510256122776464112\)
\(\displaystyle a(30) = 144171031317255718864\)
\(\displaystyle a(31) = 784899265948564770342\)
\(\displaystyle a(32) = 4277631137568917968104\)
\(\displaystyle a(33) = 23336132896728328067802\)
\(\displaystyle a(34) = 127430724958967422776764\)
\(\displaystyle a(35) = 696503831037791664366005\)
\(\displaystyle a(36) = 3810325667437945344723416\)
\(\displaystyle a(37) = 20862951670169772699569884\)
\(\displaystyle a(38) = 114327567494889469100126186\)
\(\displaystyle a(39) = 627010512468175084449245699\)
\(\displaystyle a(40) = 3441398691199018036342268694\)
\(\displaystyle a(41) = 18902517940719892827197357863\)
\(\displaystyle a(42) = 103900474619558986886311005310\)
\(\displaystyle a(43) = 571502040073810063270171499301\)
\(\displaystyle a(44) = 3145647485598338512205100268150\)
\(\displaystyle a(45) = 17325444960966711798381706801199\)
\(\displaystyle a(46) = 95484152104977328197194233935968\)
\(\displaystyle a(47) = 526552424188323869185348962416251\)
\(\displaystyle a(48) = 2905404480038250667963523923957806\)
\(\displaystyle a(49) = 16040498190236302072512974647544938\)
\(\displaystyle a(50) = 88606852877702023409234509711896052\)
\(\displaystyle a(51) = 489719332765765315944438858985265321\)
\(\displaystyle a(52) = 2708009902722995666724160075495302788\)
\(\displaystyle a(53) = 14981979259133017499634801563649896027\)
\(\displaystyle a(54) = 82927247094158291519998586067382260870\)
\(\displaystyle a(55) = 459227474358006572656633506294023333474\)
\(\displaystyle a(56) = 2544220459939487425388971490103733015086\)
\(\displaystyle a(57) = 14101711966176397927883438703014571053197\)
\(\displaystyle a{\left(n + 58 \right)} = - \frac{28677232823881103515625 n \left(n + 1\right) \left(n + 2\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{1906624 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{76806640625 \left(n + 1\right) \left(n + 2\right) \left(2 n + 3\right) \left(1824412315333051 n^{2} + 9760245392866691 n + 13238277611242140\right) a{\left(n + 1 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{9765625 \left(n + 2\right) \left(1103676764955143285141 n^{4} + 14012722603161278331025 n^{3} + 66531641548881738716779 n^{2} + 139703368622119587750395 n + 109270931025982126330860\right) a{\left(n + 2 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{2 \left(1594 n + 87161\right) a{\left(n + 57 \right)}}{31 \left(n + 59\right)} - \frac{\left(4245719 n^{2} + 462231193 n + 12580253478\right) a{\left(n + 56 \right)}}{961 \left(n + 58\right) \left(n + 59\right)} + \frac{\left(4801441783 n^{3} + 790563629617 n^{2} + 43362755188198 n + 792359285798952\right) a{\left(n + 55 \right)}}{59582 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(954843883418 n^{4} + 186309192312055 n^{3} + 13526932945621285 n^{2} + 432458567771280020 n + 5126125832532735432\right) a{\left(n + 54 \right)}}{923521 \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{5 \left(41936854002939 n^{5} + 10775441183588087 n^{4} + 1106818155719551303 n^{3} + 56809474632161540077 n^{2} + 1456998925228823088602 n + 14937284773190097308280\right) a{\left(n + 53 \right)}}{1847042 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{10 \left(367247371395197 n^{5} + 93174091327760552 n^{4} + 9452403719078136945 n^{3} + 479300061124605555166 n^{2} + 12147536251579961311696 n + 123103856339657400804036\right) a{\left(n + 52 \right)}}{923521 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(85940647520068684 n^{5} + 21451278514594203350 n^{4} + 2141202750788544553775 n^{3} + 106836970478332025641195 n^{2} + 2664670801973467239842166 n + 26577419404209295865723160\right) a{\left(n + 51 \right)}}{923521 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{5 \left(1229393888945622496 n^{5} + 301511812764688686455 n^{4} + 29572676286883040951546 n^{3} + 1449972594203509875588073 n^{2} + 35539528362502643561193486 n + 348366228981133167397961256\right) a{\left(n + 50 \right)}}{3694084 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15 \left(2959018361606863259 n^{5} + 712540672204753288666 n^{4} + 68621697458132715114921 n^{3} + 3303796884422777460743334 n^{2} + 79518025604407405561624376 n + 765435288158731499048481808\right) a{\left(n + 49 \right)}}{1847042 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(2133725262034938358247 n^{5} + 504237172547395767630435 n^{4} + 47657899425879759938969615 n^{3} + 2251900403843649113997178245 n^{2} + 53195913581102167759697673218 n + 502588723559728800926215010400\right) a{\left(n + 48 \right)}}{7388168 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(21735947375478354792313 n^{5} + 5039034866645259906121050 n^{4} + 467231469965998323168559735 n^{3} + 21659253574983843351262414710 n^{2} + 501975246066452811491434975792 n + 4653066629847748053067131249840\right) a{\left(n + 47 \right)}}{7388168 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(47465899354663238267558 n^{5} + 10792057021056605999541230 n^{4} + 981417362803763751975636195 n^{3} + 44621180279152654338775275220 n^{2} + 1014301337752677161053912237807 n + 9221941919528336700079853546070\right) a{\left(n + 46 \right)}}{1847042 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{1953125 \left(138011409844141254406873 n^{5} + 2696700136465755237854538 n^{4} + 21011350194926928854087755 n^{3} + 81512834446497026481274290 n^{2} + 157305488289551684345729152 n + 120711469683032077635583392\right) a{\left(n + 3 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(2863147673727040694021101 n^{5} + 638343040238126968234697240 n^{4} + 56924745379420447081838487095 n^{3} + 2538022416800191038787191695920 n^{2} + 56576748749785338879252250069644 n + 504451564844145652780003395809040\right) a{\left(n + 45 \right)}}{14776336 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{390625 \left(3154624750205085331321013 n^{5} + 76907898504856430015870523 n^{4} + 749202466578953536551411149 n^{3} + 3643048067076267029211064809 n^{2} + 8837230600900337584184306714 n + 8551024721640945418433710872\right) a{\left(n + 4 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(9336617823787499446330681 n^{5} + 2041297646861825936456865985 n^{4} + 178511618103713067813534264285 n^{3} + 7805139814020173953852604029715 n^{2} + 170627713903577427420237945180014 n + 1491982619726058155636157020843880\right) a{\left(n + 44 \right)}}{7388168 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{234375 \left(74938401379220610714874445 n^{5} + 2189344619315457398840396150 n^{4} + 25582101835476404448273902815 n^{3} + 149383341724333143432935888582 n^{2} + 435757272117051321279282167448 n + 507807651709931111155575146240\right) a{\left(n + 5 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(104958685410378466828802537 n^{5} + 22512287571854303618778051690 n^{4} + 1931364371165454520709925254735 n^{3} + 82844280559179203531967587401110 n^{2} + 1776703457009491039997091639026048 n + 15240942614631460104871379902152960\right) a{\left(n + 43 \right)}}{14776336 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(250898960335875109279494943 n^{5} + 52858413975663390603464114960 n^{4} + 4454026764274537815603405298685 n^{3} + 187639916467909782770065087213060 n^{2} + 3952133817373092441632960145252132 n + 33293721496045345275085947466045980\right) a{\left(n + 42 \right)}}{7388168 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15625 \left(1624992320512163666788866589 n^{5} + 55325972061826959559895923934 n^{4} + 753728446508391767879619160973 n^{3} + 5134511367690771404956179943732 n^{2} + 17485030582779630715893752737008 n + 23806598635607035335164788272264\right) a{\left(n + 6 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{3 \left(1915750955750393627433805137 n^{5} + 396766305293657148187571880395 n^{4} + 32822432661418694962825795402105 n^{3} + 1355806316305014060842948066649805 n^{2} + 27967400957154493895521051706120038 n + 230492779096989408438744244304796760\right) a{\left(n + 40 \right)}}{14776336 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(1971634846885264099442454702 n^{5} + 409388151833818015291902393605 n^{4} + 33991944966238770575033298623080 n^{3} + 1410787537414970715210132169616635 n^{2} + 29268123204569490318617772998829818 n + 242811089916092664764495382339502800\right) a{\left(n + 41 \right)}}{14776336 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15 \left(7112826152088878601641313411 n^{5} + 1188550731640417062458112436923 n^{4} + 78005094700351322310409146014892 n^{3} + 2498049212177734386502162922604665 n^{2} + 38650136172838307817725441605742665 n + 227113722105760361456212687327274892\right) a{\left(n + 38 \right)}}{29552672 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(13779579972634905938326711597 n^{5} + 3176235872593800780658842027130 n^{4} + 285686782730834926925449000543995 n^{3} + 12612572118405142856695096818325550 n^{2} + 274445497193929581894002691701206568 n + 2361523744780436740215009204816865920\right) a{\left(n + 39 \right)}}{29552672 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{3125 \left(39185194742169968588492653870 n^{5} + 1523289639995308687416028850903 n^{4} + 23699844824155781190124685304446 n^{3} + 184432992930628393139810311468441 n^{2} + 717762244718727141259953102405468 n + 1117332952221259883757665167542432\right) a{\left(n + 7 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{625 \left(1607927743753881907097122843535 n^{5} + 70261032755060914404808688984819 n^{4} + 1228873787640205499397520792846935 n^{3} + 10752195745837047389554027491831097 n^{2} + 47057217088069309645226416399811134 n + 82399972774545296726300540520496440\right) a{\left(n + 8 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(4160809169138192882311250566921 n^{5} + 727567936846967041737315897247195 n^{4} + 50728828692572914618188795405118245 n^{3} + 1762263244819409501778960775433161565 n^{2} + 30488017806648885303392990300679619634 n + 210033155594349857582270452586722496760\right) a{\left(n + 37 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{5 \left(4692479600269030636027528294883 n^{5} + 812611251080456227373769333542391 n^{4} + 56206689002351760690003764269512083 n^{3} + 1940804539883132438559191240632281561 n^{2} + 33451243937545232031493053897404551658 n + 230202817741690872482560312019920330608\right) a{\left(n + 36 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{125 \left(28494422747740978579341859618947 n^{5} + 1382387566156578171778449910353454 n^{4} + 26844694852204556556718536440907401 n^{3} + 260804618705525098409378013632893706 n^{2} + 1267531289452040831433365462314882612 n + 2465112341710043845082779223367813360\right) a{\left(n + 9 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(103999275984659844018138280436793 n^{5} + 17659325035493152144028390451224495 n^{4} + 1198363025773960570402803888587209975 n^{3} + 40622170481210935514305358812403461915 n^{2} + 687822177842161014428816040682493450282 n + 4653644444388548784792284120722864734960\right) a{\left(n + 35 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{25 \left(441279977019275305917460853277774 n^{5} + 23532159059197011029064432677960183 n^{4} + 502303476419722701569717025792438196 n^{3} + 5364249425706881164087816658838629197 n^{2} + 28658955481958524539124714332848935130 n + 61274494842950103778569375808221936600\right) a{\left(n + 10 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{5 \left(516710697418606445260638202682917 n^{5} + 83492215566677315019776076980439254 n^{4} + 5393930969436496365015454371660848159 n^{3} + 174152671705596068649233438565390848926 n^{2} + 2810051539369125678933153851560347853728 n + 18127642947556301228159785027398766082016\right) a{\left(n + 33 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(782899488223010109791012200166033 n^{5} + 129831280077990155607751926012020900 n^{4} + 8606815050488186272516605082992534135 n^{3} + 285098615323700806393449595045207965580 n^{2} + 4718740083433916053896957742788340501072 n + 31218578888544056665430000126980900742760\right) a{\left(n + 34 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15 \left(1608872101319192489160621271590349 n^{5} + 238298742637265843859828903779325937 n^{4} + 14115507867072012481699844813709167457 n^{3} + 417980507862250667492045518474306081901 n^{2} + 6187289621944084733759700997385232639496 n + 36628554417617969118871677523101197819656\right) a{\left(n + 30 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{25 \left(2411196507018292457267330700758267 n^{5} + 140174272284340278971968495414900526 n^{4} + 3261745607872715087238771177492821049 n^{3} + 37972407423333981541426940570060544070 n^{2} + 221157324893142734175597112094048151352 n + 515486760909009306484452915821928607872\right) a{\left(n + 11 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(7599623633069689287041322961227959 n^{5} + 1194500675061297586398819043272951475 n^{4} + 75074066241849759970031541784531505035 n^{3} + 2358359178978058808170798446230773202285 n^{2} + 37029121698851669234555097922716186315366 n + 232475411665124482347184038247668367147800\right) a{\left(n + 32 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15 \left(13980309620347778273891058141591699 n^{5} + 1941427311908539571070357356205295749 n^{4} + 107831777605546347883103697136089022655 n^{3} + 2994370229421937622972847223369432625787 n^{2} + 41571824056965113226871427733426659516294 n + 230844322521347846559565850449209992963840\right) a{\left(n + 28 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{5 \left(14636503514587830638812814501899259 n^{5} + 921182220684735822224513523480041189 n^{4} + 23205129632047622294297392413076138119 n^{3} + 292448391591566068388058755067271459003 n^{2} + 1843854082636573297838471034110097355822 n + 4652540466378255484767596777265588784248\right) a{\left(n + 12 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(20122764021646602008130527157133067 n^{5} + 3072315595443500951590031688788192310 n^{4} + 187581254316715143432018884895367802375 n^{3} + 5724894338200607861469498069166623194100 n^{2} + 87337105981988821757902805187083711632028 n + 532809651047578556419338315085864186450320\right) a{\left(n + 31 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(155062415167496725125177009647167093 n^{5} + 11246193090931378515263285111090603335 n^{4} + 326434614177285588775154950432839560325 n^{3} + 4740053577790467441238057517627040534155 n^{2} + 34431851021149685384962617437362869532772 n + 100094528034848096812579994361640575248100\right) a{\left(n + 14 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(210642484954975327938430015478665093 n^{5} + 30228920821438760878948887830097805270 n^{4} + 1734996487305060406645485597595923040035 n^{3} + 49783448189477997538185064358634090043370 n^{2} + 714139119538302919919015625363945487021352 n + 4097161903460804997193576986587081886210720\right) a{\left(n + 29 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(317805654574099518835666711366021807 n^{5} + 21526477130500816827585755347249428730 n^{4} + 583574039775280469313968035610547985905 n^{3} + 7914652465089792506207530177475198822270 n^{2} + 53699556840407580797742392414099717546648 n + 145811437785800203559762452941576860332800\right) a{\left(n + 13 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(546351582676655420261800913315371763 n^{5} + 42240458225464183650574748073925243650 n^{4} + 1306941502148409470809994397626721846215 n^{3} + 20228425717602204365389497525306499622280 n^{2} + 156618423532475071907047824480434019825812 n + 485270667798804451472871914075028037627440\right) a{\left(n + 15 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(636578467149971383287232454125886198 n^{5} + 82450344942326830175811642952777680525 n^{4} + 4271630604652043597311976234962111809320 n^{3} + 110654310091746683069716290159266472319335 n^{2} + 1433240536218389563120655744048996917884902 n + 7425719093733306163848665127365529594454560\right) a{\left(n + 26 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(763605692262549520472148812040609413 n^{5} + 102479392751295616258636097589348676250 n^{4} + 5501048319156987381511375191075550011255 n^{3} + 147641433210924851024116030933480967620210 n^{2} + 1981194883029879966296207485623971648000632 n + 10633947163241596121160601631717440295314560\right) a{\left(n + 27 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(871936059392283411364422617075803577 n^{5} + 71581611666473246931011636828426344605 n^{4} + 2351628787458571408308005575024605270905 n^{3} + 38645216622325358964115972225491930741855 n^{2} + 317673421910272939080950884901755687661498 n + 1044989524417485667449933365039607902054640\right) a{\left(n + 16 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(876941686151271200344638196944813143 n^{5} + 101186740675054770140181057008265609065 n^{4} + 4670807846419843321160362807290229851615 n^{3} + 107817498938727811741654573778247832941685 n^{2} + 1244567751347699856016024922885020861025212 n + 5747419173036702657818947608896734862498880\right) a{\left(n + 23 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(972913209335032505143941950376445913 n^{5} + 121440839195164404041202669265021621310 n^{4} + 6063656732627839712492503977094269105915 n^{3} + 151389829094299457091708152488688927170690 n^{2} + 1889965959707310625476921502216463085616852 n + 9438419972350829601076756732020262788072000\right) a{\left(n + 25 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(1034512989273892124086502321017812151 n^{5} + 114471582179741066661200497260670599040 n^{4} + 5067492944164194461932959101448933117615 n^{3} + 112185232327734535538950429351074019655210 n^{2} + 1242019516887975225454633375543474297393064 n + 5501286062134083087692953155394968798589980\right) a{\left(n + 22 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(1264345126869341396802886717384023787 n^{5} + 109834534731855415632614564884431459260 n^{4} + 3818055169562431835885295695283866073905 n^{3} + 66387472693904501772522746066854215779740 n^{2} + 577391966267737526931960201964297062677388 n + 2009487956593380066415039400314045077707040\right) a{\left(n + 17 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(1363820499160884265967165206290126561 n^{5} + 163807797183716680025333906195554071965 n^{4} + 7870626589081067926067478625484631633505 n^{3} + 189101374453919891726680216013834606272495 n^{2} + 2271924117527348211408610523518617570188474 n + 10919423182149437644155555481672506932521440\right) a{\left(n + 24 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(1669899867550553013493063261891403518 n^{5} + 153030376922496312637400983322776393085 n^{4} + 5611445876160154571703245320620681561080 n^{3} + 102918511625322761680261638544393063819375 n^{2} + 944136863772085971643659869990059290773262 n + 3465690615992231234307380953769826243044520\right) a{\left(n + 18 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(2218470852690434916003099834665113561 n^{5} + 224422507265121987628898101325334196075 n^{4} + 9083434953565159083932284867728902478225 n^{3} + 183872900186762376547712823481093868552945 n^{2} + 1861537557720797027942120006016736886318594 n + 7540576237692615548504116469161434179377680\right) a{\left(n + 20 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(4026022578843758484329965309983372599 n^{5} + 388124635667839112754697861389947141690 n^{4} + 14971194688792416273444083964060159480165 n^{3} + 288831367609997504658278316088904858253490 n^{2} + 2786999428611394258458251648620653404926696 n + 10760329586335892545998199575208971802075680\right) a{\left(n + 19 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(4476238969506222781000900397174898733 n^{5} + 474081452607035667514554135003598910410 n^{4} + 20088377791251735260871027141655107500415 n^{3} + 425698548246641042481472899139814857588250 n^{2} + 4511570885722016974882160044549643001881552 n + 19129972529120182768081550294697348222885120\right) a{\left(n + 21 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)}, \quad n \geq 58\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 111\)
\(\displaystyle a(6) = 546\)
\(\displaystyle a(7) = 2760\)
\(\displaystyle a(8) = 14152\)
\(\displaystyle a(9) = 73217\)
\(\displaystyle a(10) = 381242\)
\(\displaystyle a(11) = 1995171\)
\(\displaystyle a(12) = 10485030\)
\(\displaystyle a(13) = 55297740\)
\(\displaystyle a(14) = 292550930\)
\(\displaystyle a(15) = 1552049418\)
\(\displaystyle a(16) = 8254753736\)
\(\displaystyle a(17) = 44005185216\)
\(\displaystyle a(18) = 235086465558\)
\(\displaystyle a(19) = 1258376412334\)
\(\displaystyle a(20) = 6748344118162\)
\(\displaystyle a(21) = 36252626922701\)
\(\displaystyle a(22) = 195072072628438\)
\(\displaystyle a(23) = 1051299650526297\)
\(\displaystyle a(24) = 5674139791228478\)
\(\displaystyle a(25) = 30667973501678763\)
\(\displaystyle a(26) = 165979232714361346\)
\(\displaystyle a(27) = 899456918761173937\)
\(\displaystyle a(28) = 4880239532203966838\)
\(\displaystyle a(29) = 26510256122776464112\)
\(\displaystyle a(30) = 144171031317255718864\)
\(\displaystyle a(31) = 784899265948564770342\)
\(\displaystyle a(32) = 4277631137568917968104\)
\(\displaystyle a(33) = 23336132896728328067802\)
\(\displaystyle a(34) = 127430724958967422776764\)
\(\displaystyle a(35) = 696503831037791664366005\)
\(\displaystyle a(36) = 3810325667437945344723416\)
\(\displaystyle a(37) = 20862951670169772699569884\)
\(\displaystyle a(38) = 114327567494889469100126186\)
\(\displaystyle a(39) = 627010512468175084449245699\)
\(\displaystyle a(40) = 3441398691199018036342268694\)
\(\displaystyle a(41) = 18902517940719892827197357863\)
\(\displaystyle a(42) = 103900474619558986886311005310\)
\(\displaystyle a(43) = 571502040073810063270171499301\)
\(\displaystyle a(44) = 3145647485598338512205100268150\)
\(\displaystyle a(45) = 17325444960966711798381706801199\)
\(\displaystyle a(46) = 95484152104977328197194233935968\)
\(\displaystyle a(47) = 526552424188323869185348962416251\)
\(\displaystyle a(48) = 2905404480038250667963523923957806\)
\(\displaystyle a(49) = 16040498190236302072512974647544938\)
\(\displaystyle a(50) = 88606852877702023409234509711896052\)
\(\displaystyle a(51) = 489719332765765315944438858985265321\)
\(\displaystyle a(52) = 2708009902722995666724160075495302788\)
\(\displaystyle a(53) = 14981979259133017499634801563649896027\)
\(\displaystyle a(54) = 82927247094158291519998586067382260870\)
\(\displaystyle a(55) = 459227474358006572656633506294023333474\)
\(\displaystyle a(56) = 2544220459939487425388971490103733015086\)
\(\displaystyle a(57) = 14101711966176397927883438703014571053197\)
\(\displaystyle a{\left(n + 58 \right)} = - \frac{28677232823881103515625 n \left(n + 1\right) \left(n + 2\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{1906624 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{76806640625 \left(n + 1\right) \left(n + 2\right) \left(2 n + 3\right) \left(1824412315333051 n^{2} + 9760245392866691 n + 13238277611242140\right) a{\left(n + 1 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{9765625 \left(n + 2\right) \left(1103676764955143285141 n^{4} + 14012722603161278331025 n^{3} + 66531641548881738716779 n^{2} + 139703368622119587750395 n + 109270931025982126330860\right) a{\left(n + 2 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{2 \left(1594 n + 87161\right) a{\left(n + 57 \right)}}{31 \left(n + 59\right)} - \frac{\left(4245719 n^{2} + 462231193 n + 12580253478\right) a{\left(n + 56 \right)}}{961 \left(n + 58\right) \left(n + 59\right)} + \frac{\left(4801441783 n^{3} + 790563629617 n^{2} + 43362755188198 n + 792359285798952\right) a{\left(n + 55 \right)}}{59582 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(954843883418 n^{4} + 186309192312055 n^{3} + 13526932945621285 n^{2} + 432458567771280020 n + 5126125832532735432\right) a{\left(n + 54 \right)}}{923521 \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{5 \left(41936854002939 n^{5} + 10775441183588087 n^{4} + 1106818155719551303 n^{3} + 56809474632161540077 n^{2} + 1456998925228823088602 n + 14937284773190097308280\right) a{\left(n + 53 \right)}}{1847042 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{10 \left(367247371395197 n^{5} + 93174091327760552 n^{4} + 9452403719078136945 n^{3} + 479300061124605555166 n^{2} + 12147536251579961311696 n + 123103856339657400804036\right) a{\left(n + 52 \right)}}{923521 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(85940647520068684 n^{5} + 21451278514594203350 n^{4} + 2141202750788544553775 n^{3} + 106836970478332025641195 n^{2} + 2664670801973467239842166 n + 26577419404209295865723160\right) a{\left(n + 51 \right)}}{923521 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{5 \left(1229393888945622496 n^{5} + 301511812764688686455 n^{4} + 29572676286883040951546 n^{3} + 1449972594203509875588073 n^{2} + 35539528362502643561193486 n + 348366228981133167397961256\right) a{\left(n + 50 \right)}}{3694084 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15 \left(2959018361606863259 n^{5} + 712540672204753288666 n^{4} + 68621697458132715114921 n^{3} + 3303796884422777460743334 n^{2} + 79518025604407405561624376 n + 765435288158731499048481808\right) a{\left(n + 49 \right)}}{1847042 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(2133725262034938358247 n^{5} + 504237172547395767630435 n^{4} + 47657899425879759938969615 n^{3} + 2251900403843649113997178245 n^{2} + 53195913581102167759697673218 n + 502588723559728800926215010400\right) a{\left(n + 48 \right)}}{7388168 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(21735947375478354792313 n^{5} + 5039034866645259906121050 n^{4} + 467231469965998323168559735 n^{3} + 21659253574983843351262414710 n^{2} + 501975246066452811491434975792 n + 4653066629847748053067131249840\right) a{\left(n + 47 \right)}}{7388168 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(47465899354663238267558 n^{5} + 10792057021056605999541230 n^{4} + 981417362803763751975636195 n^{3} + 44621180279152654338775275220 n^{2} + 1014301337752677161053912237807 n + 9221941919528336700079853546070\right) a{\left(n + 46 \right)}}{1847042 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{1953125 \left(138011409844141254406873 n^{5} + 2696700136465755237854538 n^{4} + 21011350194926928854087755 n^{3} + 81512834446497026481274290 n^{2} + 157305488289551684345729152 n + 120711469683032077635583392\right) a{\left(n + 3 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(2863147673727040694021101 n^{5} + 638343040238126968234697240 n^{4} + 56924745379420447081838487095 n^{3} + 2538022416800191038787191695920 n^{2} + 56576748749785338879252250069644 n + 504451564844145652780003395809040\right) a{\left(n + 45 \right)}}{14776336 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{390625 \left(3154624750205085331321013 n^{5} + 76907898504856430015870523 n^{4} + 749202466578953536551411149 n^{3} + 3643048067076267029211064809 n^{2} + 8837230600900337584184306714 n + 8551024721640945418433710872\right) a{\left(n + 4 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(9336617823787499446330681 n^{5} + 2041297646861825936456865985 n^{4} + 178511618103713067813534264285 n^{3} + 7805139814020173953852604029715 n^{2} + 170627713903577427420237945180014 n + 1491982619726058155636157020843880\right) a{\left(n + 44 \right)}}{7388168 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{234375 \left(74938401379220610714874445 n^{5} + 2189344619315457398840396150 n^{4} + 25582101835476404448273902815 n^{3} + 149383341724333143432935888582 n^{2} + 435757272117051321279282167448 n + 507807651709931111155575146240\right) a{\left(n + 5 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(104958685410378466828802537 n^{5} + 22512287571854303618778051690 n^{4} + 1931364371165454520709925254735 n^{3} + 82844280559179203531967587401110 n^{2} + 1776703457009491039997091639026048 n + 15240942614631460104871379902152960\right) a{\left(n + 43 \right)}}{14776336 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(250898960335875109279494943 n^{5} + 52858413975663390603464114960 n^{4} + 4454026764274537815603405298685 n^{3} + 187639916467909782770065087213060 n^{2} + 3952133817373092441632960145252132 n + 33293721496045345275085947466045980\right) a{\left(n + 42 \right)}}{7388168 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15625 \left(1624992320512163666788866589 n^{5} + 55325972061826959559895923934 n^{4} + 753728446508391767879619160973 n^{3} + 5134511367690771404956179943732 n^{2} + 17485030582779630715893752737008 n + 23806598635607035335164788272264\right) a{\left(n + 6 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{3 \left(1915750955750393627433805137 n^{5} + 396766305293657148187571880395 n^{4} + 32822432661418694962825795402105 n^{3} + 1355806316305014060842948066649805 n^{2} + 27967400957154493895521051706120038 n + 230492779096989408438744244304796760\right) a{\left(n + 40 \right)}}{14776336 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(1971634846885264099442454702 n^{5} + 409388151833818015291902393605 n^{4} + 33991944966238770575033298623080 n^{3} + 1410787537414970715210132169616635 n^{2} + 29268123204569490318617772998829818 n + 242811089916092664764495382339502800\right) a{\left(n + 41 \right)}}{14776336 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15 \left(7112826152088878601641313411 n^{5} + 1188550731640417062458112436923 n^{4} + 78005094700351322310409146014892 n^{3} + 2498049212177734386502162922604665 n^{2} + 38650136172838307817725441605742665 n + 227113722105760361456212687327274892\right) a{\left(n + 38 \right)}}{29552672 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(13779579972634905938326711597 n^{5} + 3176235872593800780658842027130 n^{4} + 285686782730834926925449000543995 n^{3} + 12612572118405142856695096818325550 n^{2} + 274445497193929581894002691701206568 n + 2361523744780436740215009204816865920\right) a{\left(n + 39 \right)}}{29552672 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{3125 \left(39185194742169968588492653870 n^{5} + 1523289639995308687416028850903 n^{4} + 23699844824155781190124685304446 n^{3} + 184432992930628393139810311468441 n^{2} + 717762244718727141259953102405468 n + 1117332952221259883757665167542432\right) a{\left(n + 7 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{625 \left(1607927743753881907097122843535 n^{5} + 70261032755060914404808688984819 n^{4} + 1228873787640205499397520792846935 n^{3} + 10752195745837047389554027491831097 n^{2} + 47057217088069309645226416399811134 n + 82399972774545296726300540520496440\right) a{\left(n + 8 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(4160809169138192882311250566921 n^{5} + 727567936846967041737315897247195 n^{4} + 50728828692572914618188795405118245 n^{3} + 1762263244819409501778960775433161565 n^{2} + 30488017806648885303392990300679619634 n + 210033155594349857582270452586722496760\right) a{\left(n + 37 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{5 \left(4692479600269030636027528294883 n^{5} + 812611251080456227373769333542391 n^{4} + 56206689002351760690003764269512083 n^{3} + 1940804539883132438559191240632281561 n^{2} + 33451243937545232031493053897404551658 n + 230202817741690872482560312019920330608\right) a{\left(n + 36 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{125 \left(28494422747740978579341859618947 n^{5} + 1382387566156578171778449910353454 n^{4} + 26844694852204556556718536440907401 n^{3} + 260804618705525098409378013632893706 n^{2} + 1267531289452040831433365462314882612 n + 2465112341710043845082779223367813360\right) a{\left(n + 9 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(103999275984659844018138280436793 n^{5} + 17659325035493152144028390451224495 n^{4} + 1198363025773960570402803888587209975 n^{3} + 40622170481210935514305358812403461915 n^{2} + 687822177842161014428816040682493450282 n + 4653644444388548784792284120722864734960\right) a{\left(n + 35 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{25 \left(441279977019275305917460853277774 n^{5} + 23532159059197011029064432677960183 n^{4} + 502303476419722701569717025792438196 n^{3} + 5364249425706881164087816658838629197 n^{2} + 28658955481958524539124714332848935130 n + 61274494842950103778569375808221936600\right) a{\left(n + 10 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{5 \left(516710697418606445260638202682917 n^{5} + 83492215566677315019776076980439254 n^{4} + 5393930969436496365015454371660848159 n^{3} + 174152671705596068649233438565390848926 n^{2} + 2810051539369125678933153851560347853728 n + 18127642947556301228159785027398766082016\right) a{\left(n + 33 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(782899488223010109791012200166033 n^{5} + 129831280077990155607751926012020900 n^{4} + 8606815050488186272516605082992534135 n^{3} + 285098615323700806393449595045207965580 n^{2} + 4718740083433916053896957742788340501072 n + 31218578888544056665430000126980900742760\right) a{\left(n + 34 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15 \left(1608872101319192489160621271590349 n^{5} + 238298742637265843859828903779325937 n^{4} + 14115507867072012481699844813709167457 n^{3} + 417980507862250667492045518474306081901 n^{2} + 6187289621944084733759700997385232639496 n + 36628554417617969118871677523101197819656\right) a{\left(n + 30 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{25 \left(2411196507018292457267330700758267 n^{5} + 140174272284340278971968495414900526 n^{4} + 3261745607872715087238771177492821049 n^{3} + 37972407423333981541426940570060544070 n^{2} + 221157324893142734175597112094048151352 n + 515486760909009306484452915821928607872\right) a{\left(n + 11 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(7599623633069689287041322961227959 n^{5} + 1194500675061297586398819043272951475 n^{4} + 75074066241849759970031541784531505035 n^{3} + 2358359178978058808170798446230773202285 n^{2} + 37029121698851669234555097922716186315366 n + 232475411665124482347184038247668367147800\right) a{\left(n + 32 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{15 \left(13980309620347778273891058141591699 n^{5} + 1941427311908539571070357356205295749 n^{4} + 107831777605546347883103697136089022655 n^{3} + 2994370229421937622972847223369432625787 n^{2} + 41571824056965113226871427733426659516294 n + 230844322521347846559565850449209992963840\right) a{\left(n + 28 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{5 \left(14636503514587830638812814501899259 n^{5} + 921182220684735822224513523480041189 n^{4} + 23205129632047622294297392413076138119 n^{3} + 292448391591566068388058755067271459003 n^{2} + 1843854082636573297838471034110097355822 n + 4652540466378255484767596777265588784248\right) a{\left(n + 12 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(20122764021646602008130527157133067 n^{5} + 3072315595443500951590031688788192310 n^{4} + 187581254316715143432018884895367802375 n^{3} + 5724894338200607861469498069166623194100 n^{2} + 87337105981988821757902805187083711632028 n + 532809651047578556419338315085864186450320\right) a{\left(n + 31 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(155062415167496725125177009647167093 n^{5} + 11246193090931378515263285111090603335 n^{4} + 326434614177285588775154950432839560325 n^{3} + 4740053577790467441238057517627040534155 n^{2} + 34431851021149685384962617437362869532772 n + 100094528034848096812579994361640575248100\right) a{\left(n + 14 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(210642484954975327938430015478665093 n^{5} + 30228920821438760878948887830097805270 n^{4} + 1734996487305060406645485597595923040035 n^{3} + 49783448189477997538185064358634090043370 n^{2} + 714139119538302919919015625363945487021352 n + 4097161903460804997193576986587081886210720\right) a{\left(n + 29 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(317805654574099518835666711366021807 n^{5} + 21526477130500816827585755347249428730 n^{4} + 583574039775280469313968035610547985905 n^{3} + 7914652465089792506207530177475198822270 n^{2} + 53699556840407580797742392414099717546648 n + 145811437785800203559762452941576860332800\right) a{\left(n + 13 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(546351582676655420261800913315371763 n^{5} + 42240458225464183650574748073925243650 n^{4} + 1306941502148409470809994397626721846215 n^{3} + 20228425717602204365389497525306499622280 n^{2} + 156618423532475071907047824480434019825812 n + 485270667798804451472871914075028037627440\right) a{\left(n + 15 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(636578467149971383287232454125886198 n^{5} + 82450344942326830175811642952777680525 n^{4} + 4271630604652043597311976234962111809320 n^{3} + 110654310091746683069716290159266472319335 n^{2} + 1433240536218389563120655744048996917884902 n + 7425719093733306163848665127365529594454560\right) a{\left(n + 26 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(763605692262549520472148812040609413 n^{5} + 102479392751295616258636097589348676250 n^{4} + 5501048319156987381511375191075550011255 n^{3} + 147641433210924851024116030933480967620210 n^{2} + 1981194883029879966296207485623971648000632 n + 10633947163241596121160601631717440295314560\right) a{\left(n + 27 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(871936059392283411364422617075803577 n^{5} + 71581611666473246931011636828426344605 n^{4} + 2351628787458571408308005575024605270905 n^{3} + 38645216622325358964115972225491930741855 n^{2} + 317673421910272939080950884901755687661498 n + 1044989524417485667449933365039607902054640\right) a{\left(n + 16 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(876941686151271200344638196944813143 n^{5} + 101186740675054770140181057008265609065 n^{4} + 4670807846419843321160362807290229851615 n^{3} + 107817498938727811741654573778247832941685 n^{2} + 1244567751347699856016024922885020861025212 n + 5747419173036702657818947608896734862498880\right) a{\left(n + 23 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(972913209335032505143941950376445913 n^{5} + 121440839195164404041202669265021621310 n^{4} + 6063656732627839712492503977094269105915 n^{3} + 151389829094299457091708152488688927170690 n^{2} + 1889965959707310625476921502216463085616852 n + 9438419972350829601076756732020262788072000\right) a{\left(n + 25 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(1034512989273892124086502321017812151 n^{5} + 114471582179741066661200497260670599040 n^{4} + 5067492944164194461932959101448933117615 n^{3} + 112185232327734535538950429351074019655210 n^{2} + 1242019516887975225454633375543474297393064 n + 5501286062134083087692953155394968798589980\right) a{\left(n + 22 \right)}}{118210688 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(1264345126869341396802886717384023787 n^{5} + 109834534731855415632614564884431459260 n^{4} + 3818055169562431835885295695283866073905 n^{3} + 66387472693904501772522746066854215779740 n^{2} + 577391966267737526931960201964297062677388 n + 2009487956593380066415039400314045077707040\right) a{\left(n + 17 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(1363820499160884265967165206290126561 n^{5} + 163807797183716680025333906195554071965 n^{4} + 7870626589081067926067478625484631633505 n^{3} + 189101374453919891726680216013834606272495 n^{2} + 2271924117527348211408610523518617570188474 n + 10919423182149437644155555481672506932521440\right) a{\left(n + 24 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(1669899867550553013493063261891403518 n^{5} + 153030376922496312637400983322776393085 n^{4} + 5611445876160154571703245320620681561080 n^{3} + 102918511625322761680261638544393063819375 n^{2} + 944136863772085971643659869990059290773262 n + 3465690615992231234307380953769826243044520\right) a{\left(n + 18 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} - \frac{\left(2218470852690434916003099834665113561 n^{5} + 224422507265121987628898101325334196075 n^{4} + 9083434953565159083932284867728902478225 n^{3} + 183872900186762376547712823481093868552945 n^{2} + 1861537557720797027942120006016736886318594 n + 7540576237692615548504116469161434179377680\right) a{\left(n + 20 \right)}}{236421376 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(4026022578843758484329965309983372599 n^{5} + 388124635667839112754697861389947141690 n^{4} + 14971194688792416273444083964060159480165 n^{3} + 288831367609997504658278316088904858253490 n^{2} + 2786999428611394258458251648620653404926696 n + 10760329586335892545998199575208971802075680\right) a{\left(n + 19 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)} + \frac{\left(4476238969506222781000900397174898733 n^{5} + 474081452607035667514554135003598910410 n^{4} + 20088377791251735260871027141655107500415 n^{3} + 425698548246641042481472899139814857588250 n^{2} + 4511570885722016974882160044549643001881552 n + 19129972529120182768081550294697348222885120\right) a{\left(n + 21 \right)}}{472842752 \left(n + 55\right) \left(n + 56\right) \left(n + 57\right) \left(n + 58\right) \left(n + 59\right)}, \quad n \geq 58\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 111 rules.
Finding the specification took 2120 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_{32}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{32}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{32}\! \left(x \right) F_{85}\! \left(x \right)}\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{84} \left(x \right)^{2} F_{17}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{21}\! \left(x \right) &= -F_{76}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right) F_{32}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{24}\! \left(x \right) &= \frac{F_{25}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{32}\! \left(x \right) F_{34}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{32}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{32}\! \left(x \right) &= x\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{32}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{32}\! \left(x \right) F_{34}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{32}\! \left(x \right) F_{33}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{33}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= -F_{54}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= \frac{F_{45}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= -F_{53}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{52}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{2}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{28}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{32}\! \left(x \right) F_{34}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{32}\! \left(x \right) F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{33}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{39}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{68}\! \left(x \right) &= 0\\
F_{69}\! \left(x \right) &= F_{32}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{32}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{32}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{33}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{33}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{32}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= \frac{F_{82}\! \left(x \right)}{F_{32}\! \left(x \right)}\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= -F_{30}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{84} \left(x \right)^{2} F_{32}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{0}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{32}\! \left(x \right) F_{34}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{32}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{37}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{33}\! \left(x \right) F_{65}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{0}\! \left(x \right) F_{32}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{33}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{104}\! \left(x \right) &= -F_{14}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= \frac{F_{106}\! \left(x \right)}{F_{32}\! \left(x \right) F_{84}\! \left(x \right)}\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{32}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{110}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{20}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{23}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 114 rules.
Finding the specification took 1143 seconds.
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Copy 114 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_{21}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{21}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{21}\! \left(x \right) F_{86}\! \left(x \right)}\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{21}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{17}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= x\\
F_{22}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{21}\! \left(x \right) F_{25}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{25}\! \left(x \right) &= \frac{F_{26}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{21}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{21}\! \left(x \right) F_{34}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{21}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{21}\! \left(x \right) F_{33}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{33}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= -F_{57}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= \frac{F_{45}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= -F_{54}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{21}\! \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_{51}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= \frac{F_{53}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{53}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{2}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{56}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{29}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{21}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{33}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{39}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{71}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{70}\! \left(x \right) &= 0\\
F_{71}\! \left(x \right) &= F_{21}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{21}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \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_{77}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{33}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{33}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{21}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{22}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{21}\! \left(x \right)}\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88} \left(x \right)^{2} F_{21}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{0}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{21}\! \left(x \right) F_{34}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{21}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{37}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{33}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{0}\! \left(x \right) F_{21}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{102}\! \left(x \right) F_{107}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{107}\! \left(x \right) &= -F_{14}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= \frac{F_{109}\! \left(x \right)}{F_{21}\! \left(x \right) F_{88}\! \left(x \right)}\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{21}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{18}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{24}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 19 rules.
Finding the specification took 60 seconds.
Copy 19 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right) F_{8}\! \left(x \right)\\
F_{7}\! \left(x , y\right) &= -\frac{-F_{5}\! \left(x , y\right) y +F_{5}\! \left(x , 1\right)}{-1+y}\\
F_{8}\! \left(x \right) &= x\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , 1, y\right)\\
F_{11}\! \left(x , y , z\right) &= -\frac{-F_{12}\! \left(x , y z \right) y +F_{12}\! \left(x , z\right)}{-1+y}\\
F_{12}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{12}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= y x\\
F_{16}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)^{2} F_{15}\! \left(x , y\right)\\
\end{align*}\)