1, 1, 2, 6, 24, 112, 562, 2925, 15560, 84057, 459562, 2537429, 14127425, 79222292, 447042018, ...

\(\displaystyle x^{3} \left(4 x^{3}-10 x^{2}+7 x -2\right) F \left(x \right)^{6}-x^{2} \left(10 x^{3}-27 x^{2}+23 x -8\right) F \left(x \right)^{5}+x \left(8 x^{4}-21 x^{3}+9 x^{2}+10 x -9\right) F \left(x \right)^{4}-\left(-2+x \right) \left(8 x^{3}-17 x^{2}+10 x +1\right) F \left(x \right)^{3}+\left(4 x^{4}-21 x^{3}+30 x^{2}-8 x -6\right) F \left(x \right)^{2}+\left(x -1\right) \left(-2+x \right) \left(2 x +3\right) F \! \left(x \right)-\left(x -1\right) \left(-2+x \right) = 0\)

\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 562\)
\(\displaystyle a(7) = 2925\)
\(\displaystyle a(8) = 15560\)
\(\displaystyle a(9) = 84057\)
\(\displaystyle a(10) = 459562\)
\(\displaystyle a(11) = 2537429\)
\(\displaystyle a(12) = 14127425\)
\(\displaystyle a(13) = 79222292\)
\(\displaystyle a(14) = 447042018\)
\(\displaystyle a(15) = 2536551186\)
\(\displaystyle a(16) = 14463343813\)
\(\displaystyle a(17) = 82832989904\)
\(\displaystyle a(18) = 476279412635\)
\(\displaystyle a(19) = 2748436555670\)
\(\displaystyle a(20) = 15912503444657\)
\(\displaystyle a(21) = 92406258823648\)
\(\displaystyle a(22) = 538108842191647\)
\(\displaystyle a(23) = 3141612746114930\)
\(\displaystyle a(24) = 18385145904195307\)
\(\displaystyle a(25) = 107830153583816408\)
\(\displaystyle a(26) = 633733000526866141\)
\(\displaystyle a(27) = 3731694238570409215\)
\(\displaystyle a(28) = 22013326930739516649\)
\(\displaystyle a(29) = 130075766538144015070\)
\(\displaystyle a(30) = 769827958968206215136\)
\(\displaystyle a(31) = 4562857060370257583645\)
\(\displaystyle a(32) = 27082494876269420148349\)
\(\displaystyle a(33) = 160958849050328637079478\)
\(\displaystyle a(34) = 957820020811397180721392\)
\(\displaystyle a(35) = 5706459711491088457163599\)
\(\displaystyle a(36) = 34035844022008516453773393\)
\(\displaystyle a(37) = 203220887518262081479671413\)
\(\displaystyle a(38) = 1214616406611479540258508763\)
\(\displaystyle a(39) = 7266537068608404263389725569\)
\(\displaystyle a(40) = 43512441947897353111815094750\)
\(\displaystyle a(41) = 260782507413822165944651751406\)
\(\displaystyle a(42) = 1564246380779534527739541394567\)
\(\displaystyle a(43) = 9390254575369350211311304973203\)
\(\displaystyle a(44) = 56413094773531806365932274586012\)
\(\displaystyle a(45) = 339155324011006919126247193923075\)
\(\displaystyle a(46) = 2040422906658068268900063480090480\)
\(\displaystyle a(47) = 12283781252637969788479902922973569\)
\(\displaystyle a(48) = 73998434377117801231329917654180597\)
\(\displaystyle a(49) = 446046868032002673171960421500481997\)
\(\displaystyle a(50) = 2690267924665752198103273542273417461\)
\(\displaystyle a(51) = 16235206290127166017716260613405735031\)
\(\displaystyle a(52) = 98029782040661407992245678856556554690\)
\(\displaystyle a(53) = 592225945082255830049070680329882716949\)
\(\displaystyle a(54) = 3579626222750628156761878641561137612934\)
\(\displaystyle a(55) = 21647159760572698817834385654143534322798\)
\(\displaystyle a(56) = 130969357105924543014594089844509691945682\)
\(\displaystyle a(57) = 792751230416805969007648319659338865831316\)
\(\displaystyle a(58) = 4800604084783181175996613276989033946555998\)
\(\displaystyle a(59) = 29083067192249473605065902279835954147543403\)
\(\displaystyle a(60) = 176264072512007571583145211088225819610400485\)
\(\displaystyle a(61) = 1068712500231074110014119641996782520061683682\)
\(\displaystyle a(62) = 6482252834387820795872778985463047835917316298\)
\(\displaystyle a(63) = 39332701929987489807030254010333949376284874450\)
\(\displaystyle a(64) = 238747770138344506940186226556694396228138528827\)
\(\displaystyle a(65) = 1449698913083579101423469977600480187397776897083\)
\(\displaystyle a(66) = 8805716109565543638616916549128985540016128248534\)
\(\displaystyle a(67) = 53505146364430309719443643742809444912652778060771\)
\(\displaystyle a(68) = 325211776945124964390283600290923255590544185847310\)
\(\displaystyle a(69) = 1977301083734011785475225143969306773715198010596102\)
\(\displaystyle a(70) = 12025727142025498994067062991553053740405800151631427\)
\(\displaystyle a(71) = 73160761449000507865100646537354384170588092976377122\)
\(\displaystyle a(72) = 445215112209177797447830660653752395239520590776257804\)
\(\displaystyle a(73) = 2710085603883433155845435466864710873926461080847494422\)
\(\displaystyle a(74) = 16501153688932652123938890812340528586582656717805103768\)
\(\displaystyle a(75) = 100498755198367138155862476731277436286700858179569862472\)
\(\displaystyle a(76) = 612236383969340824284775386107338787036222862862750526104\)
\(\displaystyle a(77) = 3730669605977283090899164433547133322207131951355987761639\)
\(\displaystyle a(78) = 22738450900227892197879481334682320784101050476675664663507\)
\(\displaystyle a(79) = 138624095587396036209513175187208870917286325049228799275530\)
\(\displaystyle a(80) = 845313445292451250351997123765399052148721953873773516365443\)
\(\displaystyle a(81) = 5155793974516053648131018398801712949503451798104549334417446\)
\(\displaystyle a(82) = 31453550493111084560517777086745828525487402372372222943568581\)
\(\displaystyle a{\left(n + 83 \right)} = \frac{29779558400000 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{11741919 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{20971520000 \left(n + 2\right) \left(n + 3\right) \left(2 n + 3\right) \left(78075 n^{2} + 518645 n + 814306\right) a{\left(n + 1 \right)}}{3913973 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{26214400 \left(n + 3\right) \left(5600737646 n^{4} + 86598676132 n^{3} + 490343280249 n^{2} + 1204486728683 n + 1080895412620\right) a{\left(n + 2 \right)}}{3913973 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(1128830174 n + 89343616797\right) a{\left(n + 82 \right)}}{7987700 \left(n + 84\right)} - \frac{\left(1074339828625 n^{2} + 169031572814318 n + 6648544008992593\right) a{\left(n + 81 \right)}}{111827800 \left(n + 83\right) \left(n + 84\right)} + \frac{\left(329194542744687 n^{3} + 77212292690311839 n^{2} + 6036520895170225682 n + 157308980077743488216\right) a{\left(n + 80 \right)}}{782794600 \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(125603618246190455 n^{4} + 39035031651274469022 n^{3} + 4549048951911104366173 n^{2} + 235606196850856402625670 n + 4575796908055581679020720\right) a{\left(n + 79 \right)}}{9393535200 \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{6553600 \left(2060487883694 n^{5} + 49033177862827 n^{4} + 460753627134418 n^{3} + 2139002207120033 n^{2} + 4909112187115668 n + 4458091922072640\right) a{\left(n + 3 \right)}}{11741919 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{81920 \left(3701627733443639 n^{5} + 107550232226158621 n^{4} + 1237471921092206047 n^{3} + 7053760874022674243 n^{2} + 19931063075663953482 n + 22343977089399972960\right) a{\left(n + 4 \right)}}{11741919 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{4096 \left(1267193514756759721 n^{5} + 43375708364916678431 n^{4} + 589111212543545305397 n^{3} + 3970990914140658149065 n^{2} + 13291747143084166374138 n + 17681611945578930950400\right) a{\left(n + 5 \right)}}{11741919 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(15500860504936109543 n^{5} + 5983657356310899010270 n^{4} + 923877577584346060365775 n^{3} + 71319630364778949175739420 n^{2} + 2752648891432471937342696412 n + 42494209593352958662866077760\right) a{\left(n + 78 \right)}}{46967676000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(206534072625714121221 n^{5} + 78745276642031460873075 n^{4} + 12008717139882886896777625 n^{3} + 915626161161444932366910865 n^{2} + 34905142183275830553772275814 n + 532231317918316543046282073240\right) a{\left(n + 77 \right)}}{31311784000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{1024 \left(341417638840988202733 n^{5} + 13433320744094569648085 n^{4} + 209999001955485467453885 n^{3} + 1631357188689146634887275 n^{2} + 6300588397068036062058582 n + 9682077940270792095790080\right) a{\left(n + 6 \right)}}{58709595 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(2064829310154056418068 n^{5} + 777459739178879881675513 n^{4} + 117088320995398903149782644 n^{3} + 8816604865513181399096227637 n^{2} + 331926177879655339272178682814 n + 4998321074528111406840668492436\right) a{\left(n + 76 \right)}}{18787070400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(97676450864678997026104 n^{5} + 36314550403361116410375300 n^{4} + 5400277977858757843704452675 n^{3} + 401519320063373802814390896555 n^{2} + 14926290872100852044584525385916 n + 221943637089358318610297317969500\right) a{\left(n + 75 \right)}}{62623568000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{256 \left(123904681978712055703731 n^{5} + 5504988114488975258748505 n^{4} + 97268217660727828750190515 n^{3} + 854797498095109708526093375 n^{2} + 3737788451477444763148678034 n + 6508272770798353722763460880\right) a{\left(n + 7 \right)}}{489246625 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{128 \left(6682860925694523462587947 n^{5} + 330819420639137133535755770 n^{4} + 6516862825034841387091499195 n^{3} + 63887940440623123380230724730 n^{2} + 311817659656725676650360138318 n + 606338816307815609500873378320\right) a{\left(n + 8 \right)}}{1467739875 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(28799199887764456123921234 n^{5} + 10570654986110155876756608035 n^{4} + 1551925365260659125096275782700 n^{3} + 113919350618767311975112946005645 n^{2} + 4181019315073675943662313481666306 n + 61378335745572390554501284557424320\right) a{\left(n + 74 \right)}}{1502965632000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{64 \left(100881703787730384383434138 n^{5} + 5506657674247564601653819145 n^{4} + 119659306872942536786544123920 n^{3} + 1294475039363614250322084827005 n^{2} + 6974184234169615712501884018152 n + 14975239260238351200815659194780\right) a{\left(n + 9 \right)}}{1467739875 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(394693600902462485831968489 n^{5} + 141135148034288425432209055024 n^{4} + 20186618585316776123745104197895 n^{3} + 1443629051746757559296639935843456 n^{2} + 51619242325664384533032420066425296 n + 738281419740672437279257884950019168\right) a{\left(n + 72 \right)}}{200395417600 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(620432800522334051782826593 n^{5} + 224790698222575594692877661405 n^{4} + 32577088632713988329243226014525 n^{3} + 2360515526901551749457070219417235 n^{2} + 85518960670411109495284249896202722 n + 1239279366162144080722266178261916400\right) a{\left(n + 73 \right)}}{3005931264000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{32 \left(1295113194030930074567825792 n^{5} + 77312930075158319654134247470 n^{4} + 1837587670935605864904854829655 n^{3} + 21747229623634231622810740882280 n^{2} + 128199412282062068296383282576333 n + 301248611405396512409490668253630\right) a{\left(n + 10 \right)}}{1467739875 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{16 \left(4756588240907822745601037601 n^{5} + 308494776469232440507576097895 n^{4} + 7965776805415995459372868297370 n^{3} + 102413755062028034575930750202105 n^{2} + 655866710807459326452977226511289 n + 1674325820879276788103517413970240\right) a{\left(n + 11 \right)}}{489246625 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{4 \left(54275821371003917746818929959 n^{5} + 3804570363748598584493901355703 n^{4} + 106146484765034363507347278009827 n^{3} + 1474198612481472083843887147827943 n^{2} + 10196618168369554621568531482248984 n + 28110196347403803607360313954052588\right) a{\left(n + 12 \right)}}{293547975 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(201883940500105921508617658359 n^{5} + 71235391812394893116750436950870 n^{4} + 10054168344827884287497822274317705 n^{3} + 709517572324863419752683648495994930 n^{2} + 25034976819667220565822665939202020616 n + 353336596875721256818592048639238279360\right) a{\left(n + 71 \right)}}{12023725056000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{2 \left(446041865114757586537939770311 n^{5} + 33661411903522449966142239959434 n^{4} + 1010472772028669848681367347272958 n^{3} + 15092198378924157306633656718118562 n^{2} + 112215911924046414920130713759258169 n + 332444393880155884051958180272473378\right) a{\left(n + 13 \right)}}{293547975 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(1548361543630586469812420474111 n^{5} + 539027408223423746363565265201525 n^{4} + 75060012487105016735807450256898495 n^{3} + 5226080977549395582806088123978170615 n^{2} + 181933951680146007498431025598433029014 n + 2533447285683737216451515792700977113920\right) a{\left(n + 70 \right)}}{12023725056000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(5373511403261042550609412810079 n^{5} + 1845289771886185993850222960297650 n^{4} + 253473937124236256006257083111676225 n^{3} + 17409039816175329055047559316040679100 n^{2} + 597846268901146606659613476558621831846 n + 8212357349906145116909615413135350795540\right) a{\left(n + 69 \right)}}{6011862528000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(11307808669055388679267711938278 n^{5} + 3829783685948577786400559710125095 n^{4} + 518842302591382577196040549489620450 n^{3} + 35145709291509220765393936822223492295 n^{2} + 1190379663125595698265737533544418673202 n + 16127437834447152260593750604512875888900\right) a{\left(n + 68 \right)}}{2003954176000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(15771858280360244991620144320837 n^{5} + 1278424763644235549725139231722250 n^{4} + 41173699558318486307775692709580430 n^{3} + 659187880070440865656476867350913400 n^{2} + 5249901114150414174287022229101627453 n + 16648981029525607943204924728707594330\right) a{\left(n + 14 \right)}}{1467739875 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(94614748358499338434979343718177 n^{5} + 8237733968800186637181647027510870 n^{4} + 284387067273205507611331924628607665 n^{3} + 4872398424562604136966091281702765070 n^{2} + 41471473666951044966222688229794876728 n + 140401631308544693987370694586795540250\right) a{\left(n + 15 \right)}}{2935479750 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(195629600418074086782942598082167 n^{5} + 65333981218346314791346764184155635 n^{4} + 8727944388761879426992694129499150080 n^{3} + 582993339928007094149658362875419730390 n^{2} + 19471278381137556702433047852979578239868 n + 260132761072916987298575556943318787810640\right) a{\left(n + 67 \right)}}{6011862528000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(463925269995932806632110012239579 n^{5} + 43623262949921496114069613436404880 n^{4} + 1619297547591683983025754003624806600 n^{3} + 29730984154566468509639880401105014240 n^{2} + 270472241277633300429645544217910330381 n + 976631534810239128483876464918899656900\right) a{\left(n + 16 \right)}}{5870959500 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(554294653894545610707244584314049 n^{5} + 57724528289290596418314178428945190 n^{4} + 2342055491733101991564406615896070435 n^{3} + 46574614862907282438098279109632092850 n^{2} + 455875402781813489870600366387288027666 n + 1762137030462212400993740115709994328390\right) a{\left(n + 17 \right)}}{3913973000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(1034358711256448092316132607587626 n^{5} + 340566320082917006487853698000090065 n^{4} + 44854226590228568589103994070696731150 n^{3} + 2953838240294477956642039289877724659160 n^{2} + 97264016065062273297622264408530464083449 n + 1281121508826580882418718934486675832872830\right) a{\left(n + 66 \right)}}{6011862528000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(2163961750090844234331588622164902 n^{5} + 323305268140871784987830043987378925 n^{4} + 16352109240980218802675847411101948815 n^{3} + 380115491277848176309212238125139943945 n^{2} + 4195366176538028846342961610478244742983 n + 17874100054178627854713373725819000868530\right) a{\left(n + 18 \right)}}{23483838000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - 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\frac{\left(90415102755893451050594131944321812839717 n^{5} + 22566221074107187406619996756771989477778560 n^{4} + 2252697397367166795079850873407871234553507395 n^{3} + 112430641472589432731367556944612430413967926790 n^{2} + 2805472027219299279510683441451513990794866075998 n + 28000010234027483616445038679192377979726947399840\right) a{\left(n + 49 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(110372962151000810581226231848766942676781 n^{5} + 22666926608685394897701302278935331004599349 n^{4} + 1861890906319537566926106723403533623731259993 n^{3} + 76463190851484727019542763735330280623130048523 n^{2} + 1569935495282326808906361461417716135103153116746 n + 12892189174241443415174114528301503711427188481552\right) a{\left(n + 41 \right)}}{4809490022400 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(130891669873460244738587862843026347908196 n^{5} + 28510296208794187616669744307751447363718145 n^{4} + 2483967149465325016136768674234772237628959720 n^{3} + 108206117107969588676773627022764156633589530435 n^{2} + 2356769046325811476564519115431256078225468119364 n + 20531885754030024191235515062342898531996245340460\right) a{\left(n + 43 \right)}}{8015816704000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(131063152205423043601926335468837517110602 n^{5} + 32085454758805554098880821846557099973246315 n^{4} + 3141592227204746816184187675190440746754886840 n^{3} + 153786187117712945858264632263337343774435868415 n^{2} + 3763678936692390056196804640915263118244055344328 n + 36840651420368039637819921461833377912029433448200\right) a{\left(n + 48 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(160769037524725292175541165416044436804582 n^{5} + 29561074043400562118117452057943887942753335 n^{4} + 2173538659120853737178779134965760852286712940 n^{3} + 79881328795138904111770205916058271008038984035 n^{2} + 1467386783327789569766193312741265239838218124348 n + 10778174341713926307244040220578860807451602909680\right) a{\left(n + 37 \right)}}{4007908352000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(163414045526822894470762047339554166030986 n^{5} + 29258521054068844763715913780444958800174135 n^{4} + 2094806686102230341666744428327980298915045220 n^{3} + 74966272850713052860188981844096310103587529615 n^{2} + 1340940123322961065001144335347281804688030256504 n + 9590797607638231628778902840200744686353141185620\right) a{\left(n + 36 \right)}}{4007908352000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(178399264546760953857668260109921809420273 n^{5} + 42802517591283742417010447828815169786363015 n^{4} + 4107243447598838899311846373986365639667860135 n^{3} + 197037261895047286256765829020198965054505214745 n^{2} + 4725686630094540144709696035867963020603572590492 n + 45330645440328002986067962568369684569476051111360\right) a{\left(n + 47 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(195047009872890911843049832677399369920167 n^{5} + 37834681813933461653833337494258219123746965 n^{4} + 2934914563502775073712664977847645553253718785 n^{3} + 113803917115145155430488788638981208062340017920 n^{2} + 2205801470710459580679432481838262491914360916223 n + 17096351931547523856905293929379655680550407022490\right) a{\left(n + 39 \right)}}{6011862528000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(281455227551583812196132192022967519994662 n^{5} + 64603458087743745793854149291131312877491465 n^{4} + 5930814442895318065751275565597527647141057850 n^{3} + 272204666313165575420028012213903041242378728065 n^{2} + 6245970936552570653927067181084264394439137062458 n + 57321558991366539782033173222911653436182460666300\right) a{\left(n + 45 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(334578523478508106303758925718077150049404 n^{5} + 74896589051342138058448314042436245445474775 n^{4} + 6705927420143581264709754341735723862239359910 n^{3} + 300190875825546993126046396568534678296706861995 n^{2} + 6718571557597782335872429351522212788492163341016 n + 60143154819664269070898877351621896878475588633820\right) a{\left(n + 44 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} + \frac{\left(462854431367983026679140289917476741317322 n^{5} + 97922931988223658419783270989627900698445345 n^{4} + 8286703189274273949347481861949325707772636200 n^{3} + 350624933128715955818098526675552788968626421515 n^{2} + 7417602004033860779209311745846771367890787528778 n + 62766786842084313266650757782594746813530826928200\right) a{\left(n + 42 \right)}}{24047450112000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)} - \frac{\left(463447629540611963850561669320871678500681 n^{5} + 80758585089633037404788837077979896844404615 n^{4} + 5627320835060492275404871731486998674157935075 n^{3} + 195993409634292423671582245812741455161061020205 n^{2} + 3411923610523408168966518334566162044404319946444 n + 23749566345021771340946032296612210920866444816980\right) a{\left(n + 35 \right)}}{12023725056000 \left(n + 80\right) \left(n + 81\right) \left(n + 82\right) \left(n + 83\right) \left(n + 84\right)}, \quad n \geq 83\)