1, 1, 2, 6, 24, 112, 563, 2947, 15837, 86762, 482543, 2716942, 15455752, 88696106, 512867318, ...

\(\displaystyle x^{3} \left(5 x -1\right) \left(x -1\right)^{3} F \left(x \right)^{6}+x^{2} \left(8 x^{3}-25 x^{2}+32 x -7\right) \left(x -1\right)^{2} F \left(x \right)^{5}-x \left(x -1\right) \left(4 x^{5}-28 x^{4}+55 x^{3}-20 x^{2}-22 x +7\right) F \left(x \right)^{4}+\left(x -1\right) \left(8 x^{5}-20 x^{4}+61 x^{3}-79 x^{2}+17 x +1\right) F \left(x \right)^{3}+\left(-4 x^{6}+23 x^{5}-74 x^{4}+129 x^{3}-89 x^{2}+11 x +3\right) F \left(x \right)^{2}+\left(2 x^{5}+9 x^{4}-40 x^{3}+35 x^{2}-2 x -3\right) F \! \left(x \right)-\left(x -1\right) \left(x^{4}-x^{3}-5 x^{2}+x +1\right) = 0\)

\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 563\)
\(\displaystyle a(7) = 2947\)
\(\displaystyle a(8) = 15837\)
\(\displaystyle a(9) = 86762\)
\(\displaystyle a(10) = 482543\)
\(\displaystyle a(11) = 2716942\)
\(\displaystyle a(12) = 15455752\)
\(\displaystyle a(13) = 88696106\)
\(\displaystyle a(14) = 512867318\)
\(\displaystyle a(15) = 2985205577\)
\(\displaystyle a(16) = 17477133520\)
\(\displaystyle a(17) = 102851027785\)
\(\displaystyle a(18) = 608065740854\)
\(\displaystyle a(19) = 3609881840310\)
\(\displaystyle a(20) = 21511081237509\)
\(\displaystyle a(21) = 128619966319512\)
\(\displaystyle a(22) = 771438346584929\)
\(\displaystyle a(23) = 4640095485890194\)
\(\displaystyle a(24) = 27982430213127708\)
\(\displaystyle a(25) = 169156369969889653\)
\(\displaystyle a(26) = 1024842703697589225\)
\(\displaystyle a(27) = 6221885359218132729\)
\(\displaystyle a(28) = 37846005697338442863\)
\(\displaystyle a(29) = 230618957153546838324\)
\(\displaystyle a(30) = 1407654361439084652049\)
\(\displaystyle a(31) = 8605519873029808532237\)
\(\displaystyle a(32) = 52686149596680594088175\)
\(\displaystyle a(33) = 323010036310050019085628\)
\(\displaystyle a(34) = 1982900937404366538215955\)
\(\displaystyle a(35) = 12187640423219062592623295\)
\(\displaystyle a(36) = 74996783434585995905259395\)
\(\displaystyle a(37) = 462001240352603716382937728\)
\(\displaystyle a(38) = 2849025566627786038376863114\)
\(\displaystyle a(39) = 17586496637636300508593706259\)
\(\displaystyle a(40) = 108660294628836815580557611065\)
\(\displaystyle a(41) = 671972174575670324202308343234\)
\(\displaystyle a(42) = 4159127798694319940088205126371\)
\(\displaystyle a(43) = 25763612735971150419413374189930\)
\(\displaystyle a(44) = 159716170133189896039556421844384\)
\(\displaystyle a(45) = 990863416162314423278892871899110\)
\(\displaystyle a(46) = 6151592976967929065331693945611312\)
\(\displaystyle a(47) = 38217059661774751516754073667136366\)
\(\displaystyle a(48) = 237580405809212097192735237997388505\)
\(\displaystyle a(49) = 1477869793998333521617297254943903125\)
\(\displaystyle a(50) = 9198629823229226007945469712038671905\)
\(\displaystyle a(51) = 57287697714356044979649754698441381377\)
\(\displaystyle a(52) = 356977855001897897543994510592555689656\)
\(\displaystyle a(53) = 2225634375685718738097867967983741292932\)
\(\displaystyle a(54) = 13883228139965797356726141922087482329762\)
\(\displaystyle a(55) = 86644921717075319730343555258257934817735\)
\(\displaystyle a(56) = 541008549246914200638309252290079912762572\)
\(\displaystyle a(57) = 3379607385852252280071633026090178724446323\)
\(\displaystyle a(58) = 21121395079280790004752578087954651663948312\)
\(\displaystyle a(59) = 132058586074877964953995600376201629801074284\)
\(\displaystyle a(60) = 826023055643454366679747000648820573077782912\)
\(\displaystyle a(61) = 5168842182604891156930394483842672565472322329\)
\(\displaystyle a(62) = 32356707930052925345123914281559939301601920740\)
\(\displaystyle a(63) = 202628244244831500474354179014506946557129633973\)
\(\displaystyle a(64) = 1269390143928357643170054787087281972829361010646\)
\(\displaystyle a(65) = 7955085955435398914030826892710035080625553101537\)
\(\displaystyle a(66) = 49870599763258552475755704131317252826251396940936\)
\(\displaystyle a(67) = 312744599356511407617695436997698022083148500376084\)
\(\displaystyle a(68) = 1961897469562481041622573186006168934616028043130116\)
\(\displaystyle a(69) = 12311188682033356467645683687376923108287794954698583\)
\(\displaystyle a(70) = 77278194084634691879636302495966463991299122351743782\)
\(\displaystyle a(71) = 485225377449390195933084595099727844476480728228088393\)
\(\displaystyle a(72) = 3047586465669691945659342201527351134329709149136995814\)
\(\displaystyle a(73) = 19146576102235803048549703364989776656054122485920167089\)
\(\displaystyle a(74) = 120322119027953869834937378906329016550531517773217338947\)
\(\displaystyle a(75) = 756338003341919491026079720915986784413105939632083349701\)
\(\displaystyle a(76) = 4755535599206481358395845724030271658808670989941781959281\)
\(\displaystyle a(77) = 29908394094312387565840484833427644759827217612636309580316\)
\(\displaystyle a(78) = 188145608796717611815067944642887819766002774586710749441241\)
\(\displaystyle a(79) = 1183858265251835233920970988504301762740084753818930044418221\)
\(\displaystyle a(80) = 7450876496184568559154136068526917302502050950875635324263744\)
\(\displaystyle a(81) = 46904503484857652490955570103713250818721433595253320203866196\)
\(\displaystyle a(82) = 295337660812060615245426259927181620601024142649509251869024287\)
\(\displaystyle a(83) = 1860021224739366110708402504064885023173914193584444212765412915\)
\(\displaystyle a(84) = 11716813182208694496949546251162848930469545062608226118881747897\)
\(\displaystyle a(85) = 73822964410495156020810170237576479331863748988854904217105782431\)
\(\displaystyle a{\left(n + 86 \right)} = \frac{156982445452264000 n \left(n + 1\right) \left(n + 2\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{4429 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{82067734600 \left(n + 1\right) \left(n + 2\right) \left(2 n + 3\right) \left(209409661 n^{2} + 1048246083 n + 1339003020\right) a{\left(n + 1 \right)}}{4429 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{10258466825 \left(n + 2\right) \left(381419694809 n^{4} + 4633588079352 n^{3} + 21162955383971 n^{2} + 42952978679068 n + 32613881956320\right) a{\left(n + 2 \right)}}{17716 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{9 \left(299489 n + 24639503\right) a{\left(n + 85 \right)}}{17716 \left(n + 87\right)} - \frac{\left(395052641 n^{2} + 64623210268 n + 2642783514702\right) a{\left(n + 84 \right)}}{35432 \left(n + 86\right) \left(n + 87\right)} + \frac{\left(148323459932 n^{3} + 36181602439896 n^{2} + 2941978771696699 n + 79737974189487870\right) a{\left(n + 83 \right)}}{283456 \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(9990987815726 n^{4} + 3230625785455282 n^{3} + 391729932622225774 n^{2} + 21110333607412748723 n + 426604667391774602190\right) a{\left(n + 82 \right)}}{566912 \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(512078889394913 n^{5} + 205783102316290895 n^{4} + 33077203699393541410 n^{3} + 2658301689151889163865 n^{2} + 106815997060707638192127 n + 1716781482300794329776330\right) a{\left(n + 81 \right)}}{1133824 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{120687845 \left(1281597601517221 n^{5} + 24272854148157442 n^{4} + 183953524476031945 n^{3} + 696296123444436680 n^{2} + 1314700983013188844 n + 989512030438199328\right) a{\left(n + 3 \right)}}{35432 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(20599474981379051 n^{5} + 8188332625589723405 n^{4} + 1301923457215011219345 n^{3} + 103499022055729161159865 n^{2} + 4113845849165443192643194 n + 65404992145469097734349840\right) a{\left(n + 80 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{5 \left(131442881921827141 n^{5} + 51709790897537190115 n^{4} + 8136974814760142383181 n^{3} + 640203109313033033294597 n^{2} + 25184731568061594461967654 n + 396288731317038211882009440\right) a{\left(n + 79 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{120687845 \left(158012486822025767 n^{5} + 3769786625924545450 n^{4} + 36020318555542770777 n^{3} + 172144427740153864478 n^{2} + 411144734989165664920 n + 392308766193667068768\right) a{\left(n + 4 \right)}}{283456 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(8181294640357616303 n^{5} + 3189615950674479106430 n^{4} + 497402191573395023971305 n^{3} + 38782874619724970935992370 n^{2} + 1511942762103147649369126792 n + 23576742223155303885577619280\right) a{\left(n + 78 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{5 \left(28586212559559063249 n^{5} + 11461989139251996552653 n^{4} + 1832896655201469830367047 n^{3} + 146159938237637881291487905 n^{2} + 5813539239179685433298256406 n + 92290989406133095997522010936\right) a{\left(n + 76 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(36574931729397729651 n^{5} + 14194597949894043113915 n^{4} + 2203290165249775023026585 n^{3} + 170977967776048578521061085 n^{2} + 6633294167381090469592143664 n + 102927110993518782762998186100\right) a{\left(n + 77 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{7099285 \left(136676040346137104339 n^{5} + 3942974205752360448968 n^{4} + 45555438342926264751197 n^{3} + 263326203158090664146908 n^{2} + 761117274011070406167668 n + 879616358098065581843520\right) a{\left(n + 5 \right)}}{1133824 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(4889013199596118100787 n^{5} + 1730536213936007785699665 n^{4} + 244206610687995320200710235 n^{3} + 17166487425715188311061324255 n^{2} + 600809165312067254167941354218 n + 8370469613638147027467039093960\right) a{\left(n + 75 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{1419857 \left(7384840421301939539749 n^{5} + 250002873393235572701555 n^{4} + 3388481040713666339677125 n^{3} + 22975786030123473288400705 n^{2} + 77909833329367855963364546 n + 105663527876365088887559640\right) a{\left(n + 6 \right)}}{1133824 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(140648905434228200561701 n^{5} + 50647387307072286230422250 n^{4} + 7290234204999087372352577175 n^{3} + 524305525587522487332371854630 n^{2} + 18839501193309052123340925956084 n + 270563019802678934266670274440760\right) a{\left(n + 74 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{5 \left(440782655161325035836921 n^{5} + 157714096394260100383611103 n^{4} + 22564100453407866707484627229 n^{3} + 1613509070162189642524040718005 n^{2} + 57666646105631420500668382207070 n + 824065079490908278846378467187632\right) a{\left(n + 73 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{83521 \left(4679456578199769946260989 n^{5} + 181681138496371460898798240 n^{4} + 2823289214927852615361557655 n^{3} + 21945492378693423607149844080 n^{2} + 85307801822687698790600167636 n + 132644999696034201997157801280\right) a{\left(n + 7 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(26652687676403713834835047 n^{5} + 9438430970186822918571230250 n^{4} + 1336620991965447717297468771825 n^{3} + 94617900791738538342192612248550 n^{2} + 3348047412531955073449409002969448 n + 47375048572985364404311354814099520\right) a{\left(n + 72 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{83521 \left(37921362059453590464167244 n^{5} + 1658677645582947978083340935 n^{4} + 29032255426291129098234310270 n^{3} + 254152868077768207905869069965 n^{2} + 1112631860799628594246895774786 n + 1948450552013680265266303297800\right) a{\left(n + 8 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(271066998095923768253958703 n^{5} + 94864980818625230334150975185 n^{4} + 13277277723544657692107433175215 n^{3} + 928953361381808885897211428750695 n^{2} + 32490645536345219859311229505713482 n + 454454089078722084978133158621706800\right) a{\left(n + 71 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(2404936962947460955914849178 n^{5} + 831117122114182039375240831215 n^{4} + 114870682106225957203242875308100 n^{3} + 7936939437465541661453960133455025 n^{2} + 274152496352094020193859000449352722 n + 3787170915116676298924435062475396800\right) a{\left(n + 70 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{4913 \left(4569231118305217710877118441 n^{5} + 222012865753681235973038048865 n^{4} + 4316134596293726019565086586405 n^{3} + 41963736800703835373807117438955 n^{2} + 204026435204541196044792983494014 n + 396819579889127374647299952573240\right) a{\left(n + 9 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{4913 \left(7112478986110772419359946163 n^{5} + 379586775316867766826598717310 n^{4} + 8104789202224360477098744337845 n^{3} + 86538458681699090798216261497585 n^{2} + 462060819259076054870354351095537 n + 986931829470840401811644065054500\right) a{\left(n + 10 \right)}}{1133824 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(18988956607785383433625690132 n^{5} + 6476859913586702714440960005485 n^{4} + 883540032229061290124534771793230 n^{3} + 60255274210747365287288251994285395 n^{2} + 2054327720409329490144579085246148358 n + 28011660696125217026384588824928821560\right) a{\left(n + 69 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(135127888623842769773503510057 n^{5} + 45471905711415459808095650737390 n^{4} + 6119935849978359498280940270587335 n^{3} + 411779882821991703608370862185645410 n^{2} + 13851501704111314009046638044421080968 n + 186350666679887171508175155814343728560\right) a{\left(n + 68 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(437118721772125147329303108437 n^{5} + 145074300281885104650898276224960 n^{4} + 19257179186931307637825357804557675 n^{3} + 1277953657236841719370849265519152860 n^{2} + 42399122926385576864593993791151252788 n + 562609434559630673950959737651670447840\right) a{\left(n + 67 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(2587755826281368439300130154669 n^{5} + 846800911810779981921128898323230 n^{4} + 110829376123677179332650422553320095 n^{3} + 7251924068329635977116240405615217330 n^{2} + 237233266813423393198507916341275016056 n + 3103923859898027058613421335991651127060\right) a{\left(n + 66 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{289 \left(2654301937704687955500524249213 n^{5} + 154156370087106538665956037192870 n^{4} + 3581582765673795638605644868547695 n^{3} + 41609873758245291550638228998883930 n^{2} + 241724516374062893695231629456030012 n + 561736238803245804383003232371526960\right) a{\left(n + 11 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{289 \left(12865887416825136102694343068978 n^{5} + 806754982746105956965945502255045 n^{4} + 20234709620437242404058408384932080 n^{3} + 253755954303754698376192032199639795 n^{2} + 1591108032017565935676355122803540902 n + 3990590639981010827388257248858497960\right) a{\left(n + 12 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(28175494840402255688116201623511 n^{5} + 9088244021792290205068274453228135 n^{4} + 1172485790311961949268306557841637255 n^{3} + 75624704210318861372643459898712307505 n^{2} + 2438639204549908203091808596479336577674 n + 31452009748157779634322595712119618010040\right) a{\left(n + 65 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(141609177197801485828193898153241 n^{5} + 45013162709871635066348415374206430 n^{4} + 5722816903550972973457560306400954355 n^{3} + 363757310196397552132156624082637039910 n^{2} + 11559644717937746284245154337588118330024 n + 146925576342222074456167349946543557393520\right) a{\left(n + 64 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{5 \left(569794063148704151552464417064428 n^{5} + 175762906370488020922234645105877017 n^{4} + 21685193256557416696632112169335889290 n^{3} + 1337628612998850631521816801765609136211 n^{2} + 41251843784521921682721412779706607652022 n + 508833952600666326855765192442499529995400\right) a{\left(n + 62 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - 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\frac{5 \left(393365546125235202006780985873655914957 n^{5} + 49420781107275937390571475406128503219051 n^{4} + 2482239228892528330006116178660790809128541 n^{3} + 62304060234874355170252612205143350578215393 n^{2} + 781511150569029971242077613290359112484934890 n + 3919196830763563803235698228077299806352093032\right) a{\left(n + 24 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(788530785586656044582855982162945943264 n^{5} + 95865297966028097357033522621626602983185 n^{4} + 4657321791037572805157004154961292563318710 n^{3} + 113024995570039471263335619634412707591038755 n^{2} + 1370237218916023864237122136904621340543383566 n + 6639081229807282219522320074324152246105681200\right) a{\left(n + 23 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{5 \left(823170649894971086682022797002826731613 n^{5} + 114310519201387932487756429285757051262358 n^{4} + 6348890038981436338331200554036277063089764 n^{3} + 176292951566691749074840014874156634967080219 n^{2} + 2447359920708949296858073392605258251233192796 n + 13588661204076442789060076645120591360149223784\right) a{\left(n + 27 \right)}}{1133824 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(924378439442025775173296748474162460726 n^{5} + 230669904291123369799910907486060699677475 n^{4} + 23016375696055676249656380151059011829018160 n^{3} + 1147890325061726649121350621557003117180539005 n^{2} + 28614339707320980505673429980253351786514797794 n + 285219494726291875545141286298548024601932191360\right) a{\left(n + 49 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{15 \left(935754767104911621097892271708189743854 n^{5} + 134206281412820137507582590890013235015809 n^{4} + 7698758898572137089186092989570027262133622 n^{3} + 220808518357808656394298294911571004217581671 n^{2} + 3166345283561615235454007765152574991948364608 n + 18160932614368263759629819365481289509712666532\right) a{\left(n + 28 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(1300039933018898820569522153598739520374 n^{5} + 339060048537125247666046690968120176660055 n^{4} + 34723833012050956515219194195141547485301380 n^{3} + 1752725586406141647124329115285561182163835085 n^{2} + 43730486666925854489382334645295478438021509826 n + 432347694030972852192238470316555686234411381720\right) a{\left(n + 45 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{5 \left(1380534520685519505820026932363633764213 n^{5} + 276975525589411146385581932636448599546001 n^{4} + 22100851217331337124453966954729677730988065 n^{3} + 875894728529305241090938743225358850582156535 n^{2} + 17220649964529655150019658406395124606331516298 n + 134156998145750120745306082061794106813590209576\right) a{\left(n + 43 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(1419758868091904615053662700603048643568 n^{5} + 349299939329577756719351373111798166237625 n^{4} + 34354452637391112261065065725846232411433130 n^{3} + 1688442822479242306662825449692616510001225295 n^{2} + 41468289477308522109446808913486773650002095222 n + 407164065136582581814684936002026768369717195880\right) a{\left(n + 48 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(1904739259018557748633757519951708161409 n^{5} + 463809970899930287013639352334141259505590 n^{4} + 45123049340197632283743726229487393108240675 n^{3} + 2192541968941580979557078892781197383055061170 n^{2} + 53212454772323026956394601314566772971451535036 n + 516068253897941023593406532632973221608011269440\right) a{\left(n + 47 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(2063190406286389298684348534529016089653 n^{5} + 503017842571827273915202122603948269961745 n^{4} + 48906189315193382490359573481569319990390065 n^{3} + 2370919632667421987488000338418663009123093115 n^{2} + 57325851479235579700281247728794058831195167942 n + 553156649485638680902231814599366723150159701960\right) a{\left(n + 46 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(2194671845542280208544356133103876372407 n^{5} + 285159003623514724494495476824180352474600 n^{4} + 14815834745545332047550922909695649494141085 n^{3} + 384768559061465057435198254314491005184390590 n^{2} + 4994708694308259137583873678444196508830111078 n + 25926892049757821497800760069023125909254873260\right) a{\left(n + 25 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(4443281466831759170215949730670122169013 n^{5} + 596999900090897952931846514350173591346060 n^{4} + 32079279206278308654064524811184977051447485 n^{3} + 861719201907401002236865440093768109993397180 n^{2} + 11571738934473533573681582013274832748679785922 n + 62146114158814129693431458237187311648740953660\right) a{\left(n + 26 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{5 \left(10260072224051606267768311476422543433217 n^{5} + 2019390069370462578165538941571040086663301 n^{4} + 158905579690440187646629555258050060338891517 n^{3} + 6249024025119608005198898972140856140812375199 n^{2} + 122810107249013091713698649903665925139825348902 n + 964915764977196460103415152685932014650620037024\right) a{\left(n + 40 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{5 \left(12924935476384571064896288738629803274695 n^{5} + 1972397602631156940542214136770010975585706 n^{4} + 120397682411781537080623619185279461238217317 n^{3} + 3674598765553245994531272661460022897228463066 n^{2} + 56075142078343405218763138907472448971071329664 n + 342286671619306933160891014280281391140816942416\right) a{\left(n + 30 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(15753045448610860456751560602333008319704 n^{5} + 3153231985747813670048082042809529499711865 n^{4} + 252251233581323350977294281818873042453844870 n^{3} + 10080676825367702526434072199787056743179508725 n^{2} + 201236500152536178647716014925663893921831807656 n + 1605294056449323692606921801827996323232864265100\right) a{\left(n + 41 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(16698547970547412944261351239957232701569 n^{5} + 3378224869219100197430387118602112179993440 n^{4} + 272879543418082908377342854307172562435104615 n^{3} + 10999503128453103028057663462538063228946933440 n^{2} + 221219503542910460553908695384894996111623804896 n + 1775540226774210159699846398999362947138306229440\right) a{\left(n + 42 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(22119765038612728524665003583762371249751 n^{5} + 3273813579219789913101525242214918546508855 n^{4} + 193810648796329786791098766355504701609315135 n^{3} + 5736696554378305078041545121142592973447803465 n^{2} + 84899853259257503995995973309895790520392267474 n + 502577508785099485173557750332702296939823317120\right) a{\left(n + 29 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{5 \left(22145005106698789160427013959262582887603 n^{5} + 3583397603869290221422889648506460646333947 n^{4} + 231939416301154483195714565632324003429063747 n^{3} + 7506294527652246082477792494077424249719679937 n^{2} + 121464463044938017423627663921794653880834248054 n + 786206355135402667766689692807753148028653484016\right) a{\left(n + 32 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(69094475397922585913295283480881129192723 n^{5} + 12438797972855565198867227262760127274621335 n^{4} + 895655574074020995051693900890061201300061515 n^{3} + 32243553009425072068068110743548833381147896105 n^{2} + 580344337242395803211375358730839956717940682002 n + 4177932510266421061631750093443635749901556625280\right) a{\left(n + 36 \right)}}{2267648 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(74830344443609732713259210853546868112937 n^{5} + 14437840193756266735488269953507473068883790 n^{4} + 1113928881722205126950080641946081650998442235 n^{3} + 42958844149949003168293587799503790361359472150 n^{2} + 828107585080630328716173453999094185367173312728 n + 6383357616115980540963196916464892939371940807040\right) a{\left(n + 39 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(87697984315375326091773483028472207531412 n^{5} + 13787054633511822632304852150906716478994955 n^{4} + 866989882781434521594232901944935593782091310 n^{3} + 27260138571055725063923824606344058796175971725 n^{2} + 428562734025702894754082149043109279688012094118 n + 2695031533671076139559265658319753785773417237440\right) a{\left(n + 31 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(99533252267390283192351746788259603212471 n^{5} + 18789956500424839288788186187355843096650775 n^{4} + 1418603935947129114154063315770006657915938535 n^{3} + 53540836770278877993943962812240288497680907945 n^{2} + 1010179681828343158636139467701479391943074213194 n + 7622413995730221067706587912482320245638353819160\right) a{\left(n + 38 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(121887959019459932821413029827886468834451 n^{5} + 22482883537278420121147085464943322470430780 n^{4} + 1658634824754455978043536483090230483223867485 n^{3} + 61174241218818784048524085083247786663852826760 n^{2} + 1127994527755550047420293343506905199498400632164 n + 8318740954671769408620387582679418114344064020560\right) a{\left(n + 37 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(130191411971747660345806239466588831723411 n^{5} + 21665071862060647342100680371263921687272060 n^{4} + 1442098799068010886938911808129731538836995785 n^{3} + 47995262252870987196722801146530877458323032280 n^{2} + 798677731004879951481748960458936908300053276224 n + 5316257447368728786662162305077002703375012591240\right) a{\left(n + 33 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} - \frac{\left(142618163251708302095245487181561775876186 n^{5} + 24385439217413663298402335728697252250563945 n^{4} + 1667774027164005901868375423516313796066999300 n^{3} + 57030384828995962274456090949996794027589326935 n^{2} + 975078252143481766323530151902895308663552072194 n + 6668502477591022818525589758404230082089434882360\right) a{\left(n + 34 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)} + \frac{\left(145525247972457598440526820477697183287643 n^{5} + 25543763959307543318033814811686634771495975 n^{4} + 1793381895232251172847715851384239651493385935 n^{3} + 62952608456383705270999487537911225599221304785 n^{2} + 1104865677394750241904835758392794393877876904982 n + 7756250185243028635570701540583881671895679913640\right) a{\left(n + 35 \right)}}{4535296 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right)}, \quad n \geq 86\)