1, 1, 2, 6, 24, 111, 548, 2807, 14761, 79232, 432366, 2391522, 13378062, 75554024, 430207699, ...

\(\displaystyle \left(x -1\right) \left(12 x^{6}-34 x^{5}+22 x^{4}+11 x^{3}-14 x^{2}+2\right) x F \left(x \right)^{5}-x \left(x -1\right) \left(14 x^{6}-68 x^{5}+85 x^{4}-22 x^{3}-22 x^{2}+8 x +1\right) F \left(x \right)^{4}+\left(x -1\right) \left(6 x^{7}-47 x^{6}+94 x^{5}-70 x^{4}+8 x^{3}+8 x^{2}-3 x -1\right) F \left(x \right)^{3}+\left(-x^{8}+16 x^{7}-61 x^{6}+101 x^{5}-77 x^{4}+21 x^{3}+8 x^{2}-5 x -1\right) F \left(x \right)^{2}+\left(-2 x^{7}+13 x^{6}-31 x^{5}+30 x^{4}-10 x^{3}-8 x^{2}+7 x -1\right) F \! \left(x \right)-x^{6}+4 x^{5}-5 x^{4}+2 x^{3}+3 x^{2}-3 x +1 = 0\)

\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 111\)
\(\displaystyle a(6) = 548\)
\(\displaystyle a(7) = 2807\)
\(\displaystyle a(8) = 14761\)
\(\displaystyle a(9) = 79232\)
\(\displaystyle a(10) = 432366\)
\(\displaystyle a(11) = 2391522\)
\(\displaystyle a(12) = 13378062\)
\(\displaystyle a(13) = 75554024\)
\(\displaystyle a(14) = 430207699\)
\(\displaystyle a(15) = 2467079421\)
\(\displaystyle a(16) = 14236023346\)
\(\displaystyle a(17) = 82599698327\)
\(\displaystyle a(18) = 481602249973\)
\(\displaystyle a(19) = 2820306961288\)
\(\displaystyle a(20) = 16581081610569\)
\(\displaystyle a(21) = 97830810120332\)
\(\displaystyle a(22) = 579087945439528\)
\(\displaystyle a(23) = 3437933586792191\)
\(\displaystyle a(24) = 20465753270888852\)
\(\displaystyle a(25) = 122135318754932187\)
\(\displaystyle a(26) = 730558343133142083\)
\(\displaystyle a(27) = 4379198940379141215\)
\(\displaystyle a(28) = 26302348416625550662\)
\(\displaystyle a(29) = 158268769395500456961\)
\(\displaystyle a(30) = 953989186867668032869\)
\(\displaystyle a(31) = 5759582953521638768410\)
\(\displaystyle a(32) = 34825256401305424314451\)
\(\displaystyle a(33) = 210869423609420023079757\)
\(\displaystyle a(34) = 1278535244983793473587492\)
\(\displaystyle a(35) = 7761729517826473707395109\)
\(\displaystyle a(36) = 47175951229532608643875487\)
\(\displaystyle a(37) = 287059089109834638253922733\)
\(\displaystyle a(38) = 1748576859730272938460819848\)
\(\displaystyle a(39) = 10661964330049896205245153403\)
\(\displaystyle a(40) = 65073903845661204380210668501\)
\(\displaystyle a(41) = 397533105800196473989858371243\)
\(\displaystyle a(42) = 2430623344258395555548642632872\)
\(\displaystyle a(43) = 14873815303835219228488664589852\)
\(\displaystyle a(44) = 91090081714298968582200182767602\)
\(\displaystyle a(45) = 558275421437231818282360101058565\)
\(\displaystyle a(46) = 3424051992550686261475326116946555\)
\(\displaystyle a(47) = 21015186442303275967695491682400375\)
\(\displaystyle a(48) = 129066835343447736247536005832680519\)
\(\displaystyle a(49) = 793181951360002765060939149918007953\)
\(\displaystyle a(50) = 4877493160093947679657087227024394099\)
\(\displaystyle a(51) = 30010676463487122746104667007469186396\)
\(\displaystyle a(52) = 184756768557342793506577821918744928455\)
\(\displaystyle a(53) = 1138049440479075352999187801985787432756\)
\(\displaystyle a(54) = 7013735058600475010562313102269656970813\)
\(\displaystyle a(55) = 43247078165478321817538605066789245863518\)
\(\displaystyle a(56) = 266793687119387754301868577784122222852899\)
\(\displaystyle a(57) = 1646638544048579247989539076196906505344644\)
\(\displaystyle a(58) = 10167587659220687862455626430175950276284453\)
\(\displaystyle a(59) = 62809859433056899657879330757808247368077108\)
\(\displaystyle a(60) = 388169695035755939443831601614683566853267712\)
\(\displaystyle a(61) = 2399900922461798889558700096121137321577524155\)
\(\displaystyle a(62) = 14843528285546837440732860827804265484322917808\)
\(\displaystyle a(63) = 91843337816001228384072655638331584215185243305\)
\(\displaystyle a(64) = 568485836042911132858244914160750500932872050351\)
\(\displaystyle a(65) = 3520044448508630038266891429617138591966005792826\)
\(\displaystyle a(66) = 21803610450600087163364802094176060185580191188191\)
\(\displaystyle a(67) = 135100177614395261473821533996241627544020780720427\)
\(\displaystyle a(68) = 837387233870311485600290196531706415150106672221630\)
\(\displaystyle a(69) = 5192010001585018382060637273044016928774300580740947\)
\(\displaystyle a(70) = 32201752704846213150285931664794689436370704073110721\)
\(\displaystyle a(71) = 199781150522192844472384815098705606449243153137979232\)
\(\displaystyle a(72) = 1239814983095556317404320690032590441207217488403654222\)
\(\displaystyle a(73) = 7696320303210121899893300902374286017518586546020717780\)
\(\displaystyle a(74) = 47789217835569275813279187804383591204746756905232328831\)
\(\displaystyle a(75) = 296820596399384931296237571144727163900970391226468066243\)
\(\displaystyle a(76) = 1844048672638369852806329028157130819156885836631098794727\)
\(\displaystyle a(77) = 11459403072187185800343163942439073618771454164340048536833\)
\(\displaystyle a(78) = 71229521718296992994899434828851123668929499641592611328257\)
\(\displaystyle a(79) = 442857224490336871654277881475204244150049748298616140862273\)
\(\displaystyle a(80) = 2754041443777266120090447469011696801349028725713131769675658\)
\(\displaystyle a(81) = 17130802076078925421631376678432699179450359504527498848531112\)
\(\displaystyle a(82) = 106581778187271135483836910276717687528492768919658374993496834\)
\(\displaystyle a(83) = 663260146180504450799248809013025382497741069623538521509822985\)
\(\displaystyle a(84) = 4128366468289836329110884791746562823896047684182093842092365434\)
\(\displaystyle a(85) = 25701814421526503777343662559685720047850396317552250916109210487\)
\(\displaystyle a(86) = 160043634875128557609219655733813855002094007089919756272180137521\)
\(\displaystyle a(87) = 996781716725554202129877805060807809501075684477005689157756335555\)
\(\displaystyle a(88) = 6209359102666666319259532675748082141815651560574103085346745658510\)
\(\displaystyle a(89) = 38688031777188053344784526998256465679235137469226777275382378785697\)
\(\displaystyle a(90) = 241094772052200348097193858665473336581714740933883415237221957293472\)
\(\displaystyle a(91) = 1502721369249027001666640070605295129037735373321849797591488301571914\)
\(\displaystyle a(92) = 9368000713541428325041689051101695739021881456921514931381465791092763\)
\(\displaystyle a(93) = 58410574708030735732669860060172342065047123687592827486691602018142325\)
\(\displaystyle a(94) = 364259205328304537435432974284438024684882096161121602487901941994217986\)
\(\displaystyle a(95) = 2271969603077175407633288146693244517789100468860213218834966183312055939\)
\(\displaystyle a(96) = 14173134314309242042259846114626632801746733586740057859517932235420449196\)
\(\displaystyle a(97) = 88429918029957105012086530873628165214721783404451627418740149059088757390\)
\(\displaystyle a(98) = 551824589094432509492180159347721582199464891433604987185950214145047624046\)
\(\displaystyle a(99) = 3444054359008494881074771688379450609250603161617302431277483565430705935156\)
\(\displaystyle a(100) = 21498330098290079610038974948229798600561725438730667251290480469919122446604\)
\(\displaystyle a(101) = 134215889760596261106607017888161589670495926668724425274290718403850338666242\)
\(\displaystyle a(102) = 838043104142113656972988862960951863401782372797798758447013655626113217222242\)
\(\displaystyle a(103) = 5233482374077604661126064223533725227041297004938724531805461499511674867957537\)
\(\displaystyle a(104) = 32687068263191708155211227015040328599013142055963675077614329174963730455187130\)
\(\displaystyle a(105) = 204183578779892385889054248356981502016548438598760674054867268797725938863353359\)
\(\displaystyle a(106) = 1275628358286499614896241777397614938252832177547604187501534796048367564354824268\)
\(\displaystyle a(107) = 7970488474434648741385537665332338541752304597509799149136631318231425014891092656\)
\(\displaystyle a(108) = 49808339841944211483706912187075949142043235650348844959507500417541007705497879018\)
\(\displaystyle a(109) = 311296699980332188304569638699771071508240043364694406383113010756277235357433184782\)
\(\displaystyle a(110) = 1945813818298337029304769061961957675172377787603527876918981899034074301656854708795\)
\(\displaystyle a(111) = 12164139367653030754018135266440124660423066411008970610227389352475780400190533769676\)
\(\displaystyle a(112) = 76052566896912799293010315914224800321115520142019934247464525026140142231412011478050\)
\(\displaystyle a(113) = 475551794216469034920412563650006377088568300267028875628370632927424153939026931841728\)
\(\displaystyle a(114) = 2973940861457520983170780284347256492911655711452151296162397960921251555556195565686110\)
\(\displaystyle a(115) = 18600152639154074174538667298663563822422900491841281116016661903833268188140208542870217\)
\(\displaystyle a(116) = 116345478098290349898003506726091427351111547360703926302744423709691434645897838020819603\)
\(\displaystyle a(117) = 727830908834714305142168645481517671990571573758572926356918161192628260511284331553199232\)
\(\displaystyle a(118) = 4553639585144656667529479032780988282404860607621590273786431057016327722660159966179084050\)
\(\displaystyle a(119) = 28492672921487477806518948064500601045886087928332339161466614404001023275922859186279972946\)
\(\displaystyle a(120) = 178300819256692804620306167729736668295101637914304951219465609523930836394772521836213433428\)
\(\displaystyle a(121) = 1115882169318568779458874152099509358218024673571097019753626377505141534535452362581183219263\)
\(\displaystyle a(122) = 6984373495480995159700539359113307105595108946400843971240366962387360338889386063109957615919\)
\(\displaystyle a(123) = 43719981958776353404974408621858449890696594486320447760230321945700641931666747118509176534289\)
\(\displaystyle a(124) = 273700249647669439830131562411071580175888102540577110313345853708395896068624066953235211912698\)
\(\displaystyle a(125) = 1713611748059156575753768880190509646738656962720778810137186213781012134489640414025153174307764\)
\(\displaystyle a(126) = 10729784987728179076405153738979182497399642798770609766847070964819464556531705837079145926142592\)
\(\displaystyle a(127) = 67190876680270907940277442650937669914964974153110487178113623273956333214049602355040792355575527\)
\(\displaystyle a(128) = 420794117580719694786347581732337325209135321415859966490936307381775598641352963963325646284037272\)
\(\displaystyle a(129) = 2635532981844153398400383140079007878143943687113781672688530323346122281512113994094042533532634982\)
\(\displaystyle a(130) = 16508441960363432338505713920912136429222841490890568725127708742346840501877765152655929175254776316\)
\(\displaystyle a(131) = 103414625215677684709852211326355978982095795621094589680181060829581101118352246325518472599801855814\)
\(\displaystyle a(132) = 647881384543794945981106417428085793538232044111955513176022940129065460754730706659562279474293227588\)
\(\displaystyle a(133) = 4059253171381054070812790798291552265973645273373416980288653972484338698745521733949146618377359366822\)
\(\displaystyle a(134) = 25435092410556166826833312171235777367259624533037821592094152584382047183193488304623336513292125228346\)
\(\displaystyle a(135) = 159388323965895291469892030239374131764557700955810902865521263383794364063103206378185298090302918632798\)
\(\displaystyle a(136) = 998884240646520637555036752249681805933800356113444252447632256232767255976336415299784982131461215334496\)
\(\displaystyle a(137) = 6260496462181551119997754991783404737558481922629883235721837503260088580971362436447768871961295009469060\)
\(\displaystyle a(138) = 39240708196147897032608085798333829042540870725601012217711992022997478477949872778563985775374459279429636\)
\(\displaystyle a(139) = 245979464918828460409473582859928744432684709083495799209185425308264205779926326041049524503499925521781635\)
\(\displaystyle a(140) = 1542035374901649531339385575156949245633752734398416436138171305245285646367699130007677961220949351422843707\)
\(\displaystyle a(141) = 9667692198717785335994467509844326131019831894306610731573753640578621672637332756539373906747346415203826764\)
\(\displaystyle a(142) = 60615518180773500961368440717985817908714720093099977668199959601246722869991238009609676550358186993566244960\)
\(\displaystyle a(143) = 380081650877120659055347660322387908406483603248749244040734606163572796001561170405023037623405645928826976042\)
\(\displaystyle a(144) = 2383425679813567347628103933930271843054026537579419319409131684886883391227889473088135221927465342455132132612\)
\(\displaystyle a(145) = 14947119871234520385768894776870698989417369522023667025401753513922579188453371319855508614746017779984280095529\)
\(\displaystyle a(146) = 93744152258957226200420760682261068205909148501883440744810485485144620789132811890027753618795967195987404649269\)
\(\displaystyle a(147) = 587978169081721658669383520636663250182984903222371907833976116735607311110119257196212414136971284159980126722403\)
\(\displaystyle a(148) = 3688146416777514936502511983287958784789503398574726266165849625504049125715651400859107418352778877980735622952761\)
\(\displaystyle a(149) = 23135806392836449629739457913993553204082204124806004737682031771320815119384305902370336356937399969477261169497573\)
\(\displaystyle a(150) = 145141053163886442560996812331077873645664434567146670353537628219772692680155641637698694810725966778879588332494764\)
\(\displaystyle a(151) = 910593727000739149239040389627995036319666624067469854425322613399342175878770089315628937564112284366672624479673249\)
\(\displaystyle a(152) = 5713305081644002862012180484469467017609781881409938664570235100162756063087600108277278525278844355279279718968232993\)
\(\displaystyle a(153) = 35849093856994207969166844066197620649291497061065903198201751064454190075142784511927433066122107646713277164629578601\)
\(\displaystyle a(154) = 224955487902838334544404687726656667181223858821517731410513619877974663678979074888782481605556775075611443694793888917\)
\(\displaystyle a(155) = 1411699588488803021642362818361272573664984895601458847637498019895248870888046219864962291296354449558773059294101091681\)
\(\displaystyle a(156) = 8859616429411482151226850379517831213612669515850712502055459537053661676900467231456295563053546828159888125259331286932\)
\(\displaystyle a(157) = 55605038337960374875850942703505112462194163316710113306009587586938464418702884935032924855787368273192547549580547617162\)
\(\displaystyle a(158) = 349011410235013535467711090531294631987133402813745832985072331945023646781893943377340418624900788775370306163536653038025\)
\(\displaystyle a(159) = 2190740982879051437487651217673298900770327380398886149459959180242442406961270855724827589362604623003612294545551737038270\)
\(\displaystyle a(160) = 13752068981302825530426393911994686303525517067140641741356034003906510101858205911172006530798300699456414453108479916558517\)
\(\displaystyle a(161) = 86331708481112906230703797934882446916627130991910965886026713385401548945301611529375610413226479368659640708973101587542152\)
\(\displaystyle a(162) = 541997896430982530294181807023840556552996481096393198779678901921610767027022710505011681877864279952061564772901479928561410\)
\(\displaystyle a{\left(n + 163 \right)} = \frac{491520 n \left(n + 1\right) \left(n + 2\right) \left(2 n + 3\right) a{\left(n \right)}}{49 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{16384 \left(n + 1\right) \left(n + 2\right) \left(4421 n^{2} + 23699 n + 32460\right) a{\left(n + 1 \right)}}{245 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{1024 \left(n + 2\right) \left(334498 n^{3} + 4059849 n^{2} + 15469151 n + 19103460\right) a{\left(n + 2 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(2853 n^{2} + 921331 n + 74379258\right) a{\left(n + 162 \right)}}{28 \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(4553179 n^{3} + 2192957969 n^{2} + 352063611492 n + 18840275448360\right) a{\left(n + 161 \right)}}{1960 \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{512 \left(19063883 n^{4} + 269075895 n^{3} + 1444676548 n^{2} + 3484338264 n + 3171422988\right) a{\left(n + 3 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(117305785 n^{4} + 75074316312 n^{3} + 18017471492770 n^{2} + 1921821360535293 n + 76871027824481760\right) a{\left(n + 160 \right)}}{3920 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{256 \left(194879791 n^{4} + 3316401765 n^{3} + 21655599473 n^{2} + 64385652891 n + 73393460784\right) a{\left(n + 4 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{128 \left(264804436 n^{4} + 2088971145 n^{3} - 23684804680 n^{2} - 273758222625 n - 680779579332\right) a{\left(n + 5 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{64 \left(2056976758 n^{4} - 141462546315 n^{3} - 3338015542921 n^{2} - 23206435648248 n - 52295149759608\right) a{\left(n + 6 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(3269999825 n^{4} + 2091729312039 n^{3} + 501741504994271 n^{2} + 53488167219939355 n + 2138220398144739630\right) a{\left(n + 159 \right)}}{15680 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(4103642874 n^{4} + 3031427425291 n^{3} + 822371503178286 n^{2} + 97583823475772087 n + 4288061867357386642\right) a{\left(n + 158 \right)}}{31360 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{32 \left(23943254501 n^{4} + 1200738373195 n^{3} + 18449922966610 n^{2} + 114590880948096 n + 252498201119844\right) a{\left(n + 7 \right)}}{245 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(440572828768 n^{4} + 272718954061244 n^{3} + 63289093351817739 n^{2} + 6525906154791937149 n + 252267332785024550018\right) a{\left(n + 157 \right)}}{31360 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{8 \left(1591718092556 n^{4} + 177966352520823 n^{3} + 6686382470570926 n^{2} + 88586242316016747 n + 379115451935455560\right) a{\left(n + 10 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{16 \left(2007492377633 n^{4} + 86084280147897 n^{3} + 1347878961721903 n^{2} + 9184459149605043 n + 23063086272123636\right) a{\left(n + 8 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(5246130277609 n^{4} + 3258960341467806 n^{3} + 759126356620625795 n^{2} + 78583216040403590372 n + 3050278991090901180416\right) a{\left(n + 156 \right)}}{31360 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{8 \left(41319111757484 n^{4} + 1857880817351123 n^{3} + 30493349708488144 n^{2} + 218085566900949793 n + 576125174689755096\right) a{\left(n + 9 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(63960413906702 n^{4} + 39837042279079289 n^{3} + 9303443257229289025 n^{2} + 965534816695885881344 n + 37572847605690908224652\right) a{\left(n + 155 \right)}}{62720 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(539979466469777 n^{4} + 341610901625704056 n^{3} + 80970689929242330592 n^{2} + 8522627694866873737497 n + 336126262982788876331214\right) a{\left(n + 154 \right)}}{188160 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{4 \left(821340024949401 n^{4} + 42190286135909868 n^{3} + 808519526255617467 n^{2} + 6853399365186815428 n + 21686322068947266492\right) a{\left(n + 11 \right)}}{245 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(996301147815752 n^{4} + 543147024469421421 n^{3} + 109494203397280797256 n^{2} + 9634975064855207853285 n + 310369820347320082828338\right) a{\left(n + 153 \right)}}{376320 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{2 \left(14880077106124791 n^{4} + 796050009782420936 n^{3} + 15823845620408285217 n^{2} + 138735385405819162444 n + 453220542058435474524\right) a{\left(n + 12 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(15495734958960760 n^{4} + 8681220414420137762 n^{3} + 1810444768236850162325 n^{2} + 166334670059459100906289 n + 5669590314269240250298782\right) a{\left(n + 152 \right)}}{376320 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{2 \left(57688327702771877 n^{4} + 3475376276260243653 n^{3} + 78432921329431595077 n^{2} + 785099308416555966201 n + 2938828504772736197556\right) a{\left(n + 13 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{2 \left(180309237489707557 n^{4} + 10336945101759700567 n^{3} + 215224882554853145792 n^{2} + 1911070078584673451138 n + 6000079135862874348558\right) a{\left(n + 15 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{2 \left(416936384529669222 n^{4} + 25902410098281674374 n^{3} + 602008621019465085519 n^{2} + 6204815931300512148299 n + 23932826981320962013272\right) a{\left(n + 14 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(793467703501813006 n^{4} + 465903068450394133676 n^{3} + 102503025551505657964661 n^{2} + 10014228384962912135460493 n + 366546001162223187090719502\right) a{\left(n + 151 \right)}}{376320 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(10586401444904759353 n^{4} + 743405803482915320571 n^{3} + 19553854383031623893090 n^{2} + 228303494840971520496480 n + 998264165848388781044178\right) a{\left(n + 16 \right)}}{735 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(21111000297446955922 n^{4} + 12447219202867657118084 n^{3} + 2751191635160960065684205 n^{2} + 270168701476736047141141279 n + 9945414348506676491848506738\right) a{\left(n + 150 \right)}}{752640 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(60037040652049832424 n^{4} + 4364000068906021058317 n^{3} + 118828613147897636284680 n^{2} + 1436694808826739943470755 n + 6508332327339437055140952\right) a{\left(n + 17 \right)}}{1470 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(84145593041565223621 n^{4} + 49603897080867655774913 n^{3} + 10963546431379968538104101 n^{2} + 1076765770272537211322223202 n + 39649517194503496137658148994\right) a{\left(n + 149 \right)}}{376320 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(179699921880662731977 n^{4} + 14109614540606046778298 n^{3} + 414614434725570724918437 n^{2} + 5403622040129924215405588 n + 26352953779473329730638496\right) a{\left(n + 18 \right)}}{2940 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(774961698332805147236 n^{4} + 62104148328595284084675 n^{3} + 1864256314567402582789819 n^{2} + 24844966512524592918041622 n + 124036397741281261806195828\right) a{\left(n + 19 \right)}}{1470 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(862731701455222455754 n^{4} + 508525141628456662764411 n^{3} + 112385810922003005724846365 n^{2} + 11037181573007962727951767074 n + 406410896571361709362798489500\right) a{\left(n + 148 \right)}}{752640 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(3441389351689874419823 n^{4} + 283209591945394027119614 n^{3} + 8733365847764581021845805 n^{2} + 119622106855395097629037666 n + 614157906418636416699316884\right) a{\left(n + 20 \right)}}{5880 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(3924337269271014594584 n^{4} + 2343779129739995424186423 n^{3} + 524537873215021617754979815 n^{2} + 52136924020272485765972568822 n + 1941992450425444560674536372572\right) a{\left(n + 147 \right)}}{1505280 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(8100972886893976478511 n^{4} + 696900412849589048668078 n^{3} + 22420214923153979826914025 n^{2} + 319649513918073826756924826 n + 1703826604887429237936311004\right) a{\left(n + 21 \right)}}{2940 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(14986363237071235161497 n^{4} - 38169488078859806875694647 n^{3} - 3052782668928936665406403205 n^{2} - 80226826527332408872286513525 n - 699918016549487517855125047800\right) a{\left(n + 25 \right)}}{23520 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(24926940877767082757760 n^{4} + 14057837518232582128674677 n^{3} + 2971049200349934228985133301 n^{2} + 278880192887881522256447879962 n + 9809424517447212328534339112952\right) a{\left(n + 146 \right)}}{1505280 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(26469987313997906205263 n^{4} + 2670990577994684530159164 n^{3} + 100146603965278564227566725 n^{2} + 1654673027189750163953265876 n + 10169592880527371802877060560\right) a{\left(n + 23 \right)}}{11760 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(49900281418596093775082 n^{4} + 4355273429504715843102759 n^{3} + 141867365302540809609619576 n^{2} + 2043047279165605207299973683 n + 10968824410885709359173353844\right) a{\left(n + 22 \right)}}{5880 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(362563065823060081687174 n^{4} + 206623032864707853188893158 n^{3} + 44153666077374210552571153445 n^{2} + 4193092968926435556609945321405 n + 149312560871596210616529708323526\right) a{\left(n + 145 \right)}}{1505280 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(449864807616007568002656 n^{4} + 38509625978280741212636323 n^{3} + 1195337262878093805469490106 n^{2} + 15686441374463268209948195513 n + 71062349868501693001654350930\right) a{\left(n + 24 \right)}}{11760 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(1196178686262677014316167 n^{4} + 120144774540771628804174970 n^{3} + 4482763972407171707509029379 n^{2} + 73496128369439540156811589136 n + 445570232141690108035455258028\right) a{\left(n + 26 \right)}}{7840 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(2522792446137562695467907 n^{4} + 1432710888725112239152261721 n^{3} + 305102843277973046377199772516 n^{2} + 28875625897580149071672832102192 n + 1024774767125403352755929733948258\right) a{\left(n + 144 \right)}}{1505280 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(9637181965636870019308378 n^{4} + 1522930041967163976764138431 n^{3} + 82791060741295659341590780235 n^{2} + 1900026616181893666685265943766 n + 15800302014076194573341820775002\right) a{\left(n + 27 \right)}}{23520 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(24434132875594696541394110 n^{4} + 13788878280491206510052148119 n^{3} + 2917889113251965484793706422393 n^{2} + 274411972371044117195946627835282 n + 9677115674021776337873638856748372\right) a{\left(n + 143 \right)}}{3010560 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(27478364655736657609672218 n^{4} + 7400059433112177256559763703 n^{3} + 521274498381327589424465348544 n^{2} + 14262054565057516724119070788367 n + 136258557991481585175177738811668\right) a{\left(n + 29 \right)}}{94080 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(84371243305008843648799247 n^{4} + 47203746875427974020670719979 n^{3} + 9902500570278820626468681476815 n^{2} + 923178457074023608864360870661317 n + 32270998846852563948966735731652798\right) a{\left(n + 142 \right)}}{3010560 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - 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\frac{\left(3372383505665189275932336988229750703013 n^{4} + 1432385132008172023274182110436357331472354 n^{3} + 228097014743333293814722377736022230388227115 n^{2} + 16140044594679140249007271880323109263099007190 n + 428184616331541614258509536048278250401228912376\right) a{\left(n + 105 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(3387232278281895496725083792370360059278 n^{4} + 1365672642442257515895758737603753404688925 n^{3} + 206500261298061603278252352640618940800822784 n^{2} + 13878860522008622534565198463357700093540121409 n + 349832870642480854205930662879412805348314340804\right) a{\left(n + 100 \right)}}{3010560 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(3791667926202119056600018350620190703239 n^{4} + 1372610184959450425446904057983177379821482 n^{3} + 185889775660195208774035028138327757204526248 n^{2} + 11163953969041326321000498935492009559530427637 n + 250908355761859831905393574052325936227523352320\right) a{\left(n + 87 \right)}}{3010560 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(4043888054391868490708150854726145800823 n^{4} + 1522040649989010697536228581934030312433734 n^{3} + 215046755161234801446764351631261972002900905 n^{2} + 13518556066223614402641881926408782342447165462 n + 319048413547207996239694607672305488372988381908\right) a{\left(n + 95 \right)}}{6021120 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(4657750545064272491696687441372583845307 n^{4} + 1366185131293990644588919689820861623407770 n^{3} + 150240681123860848274705909826353094696979521 n^{2} + 7341688719974336080948384851474450402568053146 n + 134508022825445284901769343884259087761321998544\right) a{\left(n + 72 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(4671146889326482255473574103842463446207 n^{4} + 1496760623884175014580748530616366411698434 n^{3} + 179362823025966351282827495623998928401523721 n^{2} + 9529219641144231367223462388680005220545804694 n + 189423342016679563582473275894633728788224408016\right) a{\left(n + 76 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(4783131600497100148955112608730441519761 n^{4} + 1546493773212884715056682890432985295086670 n^{3} + 187539202856610759879010581592152516709339175 n^{2} + 10109603128047191225971955411402899867111148418 n + 204405183841022336869423239900342978115892321820\right) a{\left(n + 81 \right)}}{2007040 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(7317369123059289218429453153433644346013 n^{4} + 2565710313192785624616835867612358097962656 n^{3} + 337537014923870821389438452168513737941823514 n^{2} + 19746610481979203625935839206219151095999515945 n + 433455583287898405632901475701101743107606238340\right) a{\left(n + 88 \right)}}{3010560 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(7333790620150269881789002710978494503235 n^{4} + 2397287719889484446925671633616751895695896 n^{3} + 293884727013009961900205922105359731092914665 n^{2} + 16014447469556933467989961870311514555949600736 n + 327316561988679252996998024696149296696259340004\right) a{\left(n + 84 \right)}}{6021120 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(7544147875285576247763451993131004147743 n^{4} + 2974557645493754012251097302306522110755558 n^{3} + 439936184135546150632232594767783705724432985 n^{2} + 28927034042506738846302588694748691086637754210 n + 713484456758622145704598702074787905165763992816\right) a{\left(n + 99 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(7729178613486318546525769822160195330383 n^{4} + 3111942711811835345241964571173607590931966 n^{3} + 469503221733358735317104987519554397661226553 n^{2} + 31459809400484694679796488560491173520923145146 n + 789972940409978719265087606873320957140492901632\right) a{\left(n + 98 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(8827507539905844032442880268340206138389 n^{4} + 3167379735700031938571130419026298585288254 n^{3} + 426206194790506997702599478294252851606488101 n^{2} + 25490842404240152205147303744125436280431257172 n + 571752549451253185695496340573256594563448842868\right) a{\left(n + 89 \right)}}{2007040 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(10067406863192265071385979657283053182043 n^{4} + 4129008893192396290438559950498085734745134 n^{3} + 634979708529896365451142732954675452110965317 n^{2} + 43395783700798179595196777045453453517497767562 n + 1112049745146508152086812966863072593455892011128\right) a{\left(n + 101 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(10071858755311938624139800601760106481321 n^{4} + 2986723574391277282706886370786890782279254 n^{3} + 332152477915957622716642625733912895136712023 n^{2} + 16418106483751942902350898639562603912542259970 n + 304344373358558459267324255636211727420384144056\right) a{\left(n + 74 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(10291720398066651781956211745051152792447 n^{4} + 3321752668571884589879888125962032805701342 n^{3} + 401843109856672170659092719968684508932174219 n^{2} + 21594800518461965081912252761346775694628989816 n + 434976572566199574997966310468883468000263146584\right) a{\left(n + 79 \right)}}{6021120 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(11538588033947821719248993014002758157009 n^{4} + 3943767268050954558791651247042282445689698 n^{3} + 504897154846439504670865577709750420489557709 n^{2} + 28697198967883098843409455568319699940886747888 n + 611023697101018754917046934029198770623407880360\right) a{\left(n + 83 \right)}}{6021120 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(11544744488213134885501850371617089708773 n^{4} + 3511445574784220712671851114792184038002530 n^{3} + 400515497249179522527240950370212479757426711 n^{2} + 20303715070599937027802188443556495320145889194 n + 385987544153170072978915991142057738767219997480\right) a{\left(n + 77 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(11643489428265811685005665255312580264803 n^{4} + 4576152634902118920520907977851397715174210 n^{3} + 674442446243982683361594063303698089978466835 n^{2} + 44177720923608440806816159067035738029016763248 n + 1085151093495330933107576327751668835595535377764\right) a{\left(n + 97 \right)}}{6021120 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(12067985207320050738169858923310201369091 n^{4} + 3789360684795406264718559458085685979392514 n^{3} + 446206902942559440697117647813864463434800023 n^{2} + 23352443817800690151584915520216468478735921492 n + 458319289966805425524256124035447890233677849092\right) a{\left(n + 78 \right)}}{6021120 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(21371840848396244258817723051271715982815 n^{4} + 8172578957177437298863983767016210069431198 n^{3} + 1171400086747907118716702394718261272107190433 n^{2} + 74588562273541465894106867409318026384321315434 n + 1780242296577304276674480632452935142172003911560\right) a{\left(n + 94 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(25743651188972166796983470388033275972235 n^{4} + 9963087834088629518671718832092298827513458 n^{3} + 1446286879621495602337502117205146605177623825 n^{2} + 93333690872355647881630869241593885668667381962 n + 2259228829506405155485900842556345058251228457544\right) a{\left(n + 96 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(33843175051213759597280594013918081582713 n^{4} + 12507971998729788559072525007642538924103530 n^{3} + 1734213331368517182013575951005789394094865419 n^{2} + 106907158068628989009213384354178789168618227834 n + 2472383378193192140474923103996337980908550802552\right) a{\left(n + 92 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(39594307659408543485336661136738548566083 n^{4} + 14463646674931081592110771878996020868934318 n^{3} + 1980574834894602131418532333413037894223401097 n^{2} + 120493345302760893107927659046600207946721803374 n + 2747960198690412952195026571970338355847790377360\right) a{\left(n + 90 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(40232888925117609516322830600145696320713 n^{4} + 13344403563259223530371085336099766799743254 n^{3} + 1659562905572819760832503966580932323518290391 n^{2} + 91717515177214533378047183804643186489583558586 n + 1900595577919037821414362116334910270442668610040\right) a{\left(n + 82 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(41543688551038190475884128284455002051741 n^{4} + 15611324178036170671906162329440626001908474 n^{3} + 2199967523485636805380390413553370838111571079 n^{2} + 137791247428143244755820200710498403687643836914 n + 3236460461345462390749554120824757333668881350384\right) a{\left(n + 93 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} + \frac{\left(46823808542643435439668731211253064322097 n^{4} + 15990462789015101522838636782962525915461434 n^{3} + 2048063904047218977666173409657623138277673247 n^{2} + 116600954996713359332353322744558066040614477446 n + 2489730017112966105240068617567518892378219264512\right) a{\left(n + 85 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)} - \frac{\left(48152443294403047227555230824137793312829 n^{4} + 16792135219240521960976568110168178284631366 n^{3} + 2195362070196752432699181018648713117161512871 n^{2} + 127528683955120844078116093365294352780890684310 n + 2777328817597934336880211642782919339405816031832\right) a{\left(n + 86 \right)}}{12042240 \left(n + 161\right) \left(n + 162\right) \left(n + 163\right) \left(2 n + 327\right)}, \quad n \geq 163\)