1, 1, 2, 6, 24, 112, 568, 3028, 16692, 94296, 542900, 3173868, 18791204, 112448824, 679075704, ...

\(\displaystyle 4 x^{2} F \left(x \right)^{6}+\left(32 x^{3}-68 x^{2}+16 x -2\right) F \left(x \right)^{5}+\left(16 x^{5}-20 x^{4}-132 x^{3}+276 x^{2}-84 x +11\right) F \left(x \right)^{4}+\left(-16 x^{5}+28 x^{4}+216 x^{3}-496 x^{2}+174 x -24\right) F \left(x \right)^{3}+\left(4 x^{5}-8 x^{4}-168 x^{3}+452 x^{2}-178 x +26\right) F \left(x \right)^{2}+\left(-2 x^{4}+58 x^{3}-204 x^{2}+90 x -14\right) F \! \left(x \right)+x^{4}-6 x^{3}+36 x^{2}-18 x +3 = 0\)

\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 568\)
\(\displaystyle a(7) = 3028\)
\(\displaystyle a(8) = 16692\)
\(\displaystyle a(9) = 94296\)
\(\displaystyle a(10) = 542900\)
\(\displaystyle a(11) = 3173868\)
\(\displaystyle a(12) = 18791204\)
\(\displaystyle a(13) = 112448824\)
\(\displaystyle a(14) = 679075704\)
\(\displaystyle a(15) = 4133407792\)
\(\displaystyle a(16) = 25333151648\)
\(\displaystyle a(17) = 156207460864\)
\(\displaystyle a(18) = 968381106644\)
\(\displaystyle a(19) = 6032128924364\)
\(\displaystyle a(20) = 37736408939396\)
\(\displaystyle a(21) = 236991619184744\)
\(\displaystyle a(22) = 1493585406457976\)
\(\displaystyle a(23) = 9443108065939544\)
\(\displaystyle a(24) = 59878143978488360\)
\(\displaystyle a(25) = 380702284574747248\)
\(\displaystyle a(26) = 2426465440977233992\)
\(\displaystyle a(27) = 15500739770480348856\)
\(\displaystyle a(28) = 99231060790774595112\)
\(\displaystyle a(29) = 636494522603083487552\)
\(\displaystyle a(30) = 4090111487652434340224\)
\(\displaystyle a(31) = 26327915048953925562088\)
\(\displaystyle a(32) = 169742697623706424836744\)
\(\displaystyle a(33) = 1096013579230025743122192\)
\(\displaystyle a(34) = 7086825885626899662692052\)
\(\displaystyle a(35) = 45884163070714741841375372\)
\(\displaystyle a(36) = 297451642655025093757440452\)
\(\displaystyle a(37) = 1930556111819659612877230760\)
\(\displaystyle a(38) = 12543923684457078348066993816\)
\(\displaystyle a(39) = 81591304889987150530011285784\)
\(\displaystyle a(40) = 531239534408042119084590801128\)
\(\displaystyle a(41) = 3462192514348142315483085091152\)
\(\displaystyle a(42) = 22584278603173936241058957445720\)
\(\displaystyle a(43) = 147447263147427778119465144292648\)
\(\displaystyle a(44) = 963441371347043693059804951979448\)
\(\displaystyle a(45) = 6300220235027813406491448103408592\)
\(\displaystyle a(46) = 41229958118990064038878995266880848\)
\(\displaystyle a(47) = 270011723861287058457778617477849920\)
\(\displaystyle a(48) = 1769504446698260790036692552162562912\)
\(\displaystyle a(49) = 11603996073868856035957616889304452416\)
\(\displaystyle a(50) = 76144527119122601715510379478133937544\)
\(\displaystyle a(51) = 499958603680275128470524025114240805048\)
\(\displaystyle a(52) = 3284606139355099347407471886893926047080\)
\(\displaystyle a(53) = 21591196957500587152176278053176313303696\)
\(\displaystyle a(54) = 142005483890029711610434723869732874054960\)
\(\displaystyle a(55) = 934458057586587928401651229871790754947376\)
\(\displaystyle a{\left(n + 56 \right)} = \frac{2013265920 n \left(n - 1\right) \left(2 n - 3\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{\left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{33554432 n \left(2 n + 3\right) \left(74728 n^{3} + 270562 n^{2} + 79145 n - 119389\right) a{\left(n + 1 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(n + 54\right) \left(1225 n^{2} + 133073 n + 3605328\right) a{\left(n + 55 \right)}}{18 \left(n + 53\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(2629717 n^{4} + 549295836 n^{3} + 43009601099 n^{2} + 1496152725120 n + 19509908418900\right) a{\left(n + 53 \right)}}{72 \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(37447 n^{4} + 7948088 n^{3} + 632315491 n^{2} + 22347017250 n + 296030746800\right) a{\left(n + 54 \right)}}{18 \left(n + 52\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{8388608 \left(8635016 n^{5} + 90618704 n^{4} + 342453820 n^{3} + 574016677 n^{2} + 412856055 n + 99279810\right) a{\left(n + 2 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(134028682 n^{5} + 34396883335 n^{4} + 3530419345160 n^{3} + 181147000849085 n^{2} + 4646601602355498 n + 47668439137264920\right) a{\left(n + 52 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(506869702 n^{5} + 128546325175 n^{4} + 13040393239640 n^{3} + 661454406722645 n^{2} + 16775973213147678 n + 170194045247832600\right) a{\left(n + 51 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{2097152 \left(1097233952 n^{5} + 16419255320 n^{4} + 93284272000 n^{3} + 252726412075 n^{2} + 326625850533 n + 160879233060\right) a{\left(n + 3 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{1048576 \left(1243243676 n^{5} + 21782894054 n^{4} + 138205736821 n^{3} + 397201203667 n^{2} + 505399489707 n + 210413193318\right) a{\left(n + 4 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{262144 \left(2787787504 n^{5} + 140369414830 n^{4} - 563873203570 n^{3} - 17946168870490 n^{2} - 83418008648019 n - 115794415809135\right) a{\left(n + 5 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(6443676229 n^{5} + 1584111169180 n^{4} + 155694198750125 n^{3} + 7647188601991250 n^{2} + 187703129096079996 n + 1841913783624180240\right) a{\left(n + 50 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{32768 \left(186961125568 n^{5} - 6750356337332 n^{4} - 183121889596582 n^{3} - 1535066011807159 n^{2} - 5567311957908927 n - 7540383975500430\right) a{\left(n + 6 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(444103286557 n^{5} + 108109626396670 n^{4} + 10522636080790415 n^{3} + 511887849825790190 n^{2} + 12445595720283321408 n + 120986776796198662080\right) a{\left(n + 49 \right)}}{1440 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(872450834629 n^{5} + 217830107198215 n^{4} + 21684402459226085 n^{3} + 1076116710279935945 n^{2} + 26629171838820885126 n + 262919867636059479360\right) a{\left(n + 48 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(16666019372443 n^{5} + 3680915428743895 n^{4} + 324422224746611945 n^{3} + 14260440906686381075 n^{2} + 312563387504034129942 n + 2732229553019701929840\right) a{\left(n + 47 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{8192 \left(19315178316272 n^{5} + 1381851368454300 n^{4} + 27358571523526660 n^{3} + 237906809756147965 n^{2} + 968051993419097383 n + 1511823098961165660\right) a{\left(n + 7 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{2048 \left(217720806252872 n^{5} + 11049485796124224 n^{4} + 209500289800481808 n^{3} + 1907223551103605683 n^{2} + 8446808908459182059 n + 14658182586315081252\right) a{\left(n + 8 \right)}}{3 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(229898341683497 n^{5} + 50703115699812980 n^{4} + 4469233742633225275 n^{3} + 196806738094353207100 n^{2} + 4329660069835079787348 n + 38068221698951901107520\right) a{\left(n + 46 \right)}}{480 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(1716234289607411 n^{5} + 370461787322282630 n^{4} + 31962952148067783790 n^{3} + 1377840266177970423970 n^{2} + 29675707254259528863999 n + 255472961415664233198780\right) a{\left(n + 45 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{512 \left(26026991134785952 n^{5} + 1306081911518973320 n^{4} + 25782711940706413780 n^{3} + 251167634878020213715 n^{2} + 1209901303917990607033 n + 2308066689190599412890\right) a{\left(n + 9 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(27744066123945909 n^{5} + 5798668621234730245 n^{4} + 484188223284826964005 n^{3} + 20189515660615296896215 n^{2} + 420387382996974191592466 n + 3496712844109981440228360\right) a{\left(n + 44 \right)}}{960 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{128 \left(53652275152200332 n^{5} - 39174311374998170425 n^{4} - 1704726147259299882485 n^{3} - 27117172956015481509005 n^{2} - 190264893417518875623297 n - 498535090618002226356060\right) a{\left(n + 11 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{256 \left(91733060821287100 n^{5} + 5246856316104110182 n^{4} + 117371459344748906435 n^{3} + 1289514362805502785107 n^{2} + 6979168748595371581746 n + 14916795789662262401472\right) a{\left(n + 10 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(220956972707033389 n^{5} + 42272181623363922040 n^{4} + 3201278496394875164615 n^{3} + 119678133175696870035920 n^{2} + 2201471398250071002718236 n + 15864831462558179994201360\right) a{\left(n + 43 \right)}}{2880 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(2876564353847223497 n^{5} + 652358054648258492780 n^{4} + 58659089330489514678115 n^{3} + 2617686496816364014229740 n^{2} + 58034982964073288466685548 n + 511806506477014369310593680\right) a{\left(n + 42 \right)}}{5760 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{64 \left(27439494102212118253 n^{5} + 1202761949080050018520 n^{4} + 19271292886792837806185 n^{3} + 128021390037831296925230 n^{2} + 215977302423609593206332 n - 655205597467259592651840\right) a{\left(n + 12 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(92557465324283718253 n^{5} + 19353644133904230541330 n^{4} + 1616081231371536035865935 n^{3} + 67369223227943644843003610 n^{2} + 1402147391229329124400166592 n + 11656894918489971712617297600\right) a{\left(n + 41 \right)}}{11520 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{32 \left(306941197595026187201 n^{5} + 16498959723742913035115 n^{4} + 347676299913910644239425 n^{3} + 3565718897626250950813225 n^{2} + 17598827109665165379995034 n + 32761675610323852945824360\right) a{\left(n + 13 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(684119246962763644619 n^{5} + 138265662310827513711410 n^{4} + 11167662375070544754750805 n^{3} + 450608598316998301720399750 n^{2} + 9083210699340324483766456536 n + 73178770510147475531198167200\right) a{\left(n + 40 \right)}}{11520 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(693362120327765903863 n^{5} + 136444620475462942854952 n^{4} + 10732750223914667212929521 n^{3} + 421835384726944276960776596 n^{2} + 8284404921981907547201580804 n + 65037640339873762769796729984\right) a{\left(n + 39 \right)}}{2304 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{32 \left(1102252245843331527889 n^{5} + 66670705367577925722490 n^{4} + 1598591380165481985943820 n^{3} + 18958913595005842318340045 n^{2} + 110941362183910740409625316 n + 255365104127707911433190220\right) a{\left(n + 14 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{16 \left(2038827704410320458349 n^{5} + 135608512380989247443075 n^{4} + 3590720068583269130640045 n^{3} + 47283823230723066929013585 n^{2} + 309424123922332533009778286 n + 804243395972787958770855900\right) a{\left(n + 15 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(2114633170884457333584 n^{5} + 406689699740256959852780 n^{4} + 31265233230861976528247545 n^{3} + 1201017982372006010240253755 n^{2} + 23053424967437408808896647866 n + 176896031605850843253042641520\right) a{\left(n + 38 \right)}}{1920 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(4313399157556194897476 n^{5} + 856454101214968300606890 n^{4} + 67380060320678911567584405 n^{3} + 2629573904573331809257724035 n^{2} + 50966432864408559807662758214 n + 392848633332918419467773013440\right) a{\left(n + 36 \right)}}{1920 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{8 \left(5597898192700406302139 n^{5} + 404499976441174797165362 n^{4} + 11662768466329491285045919 n^{3} + 167696461818676241368359784 n^{2} + 1202303506630782548172249552 n + 3437801614344403925849852568\right) a{\left(n + 16 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{16 \left(13329527253422208783039 n^{5} + 1101755336224706941503985 n^{4} + 36411078302183222651974360 n^{3} + 601502384671845025747635535 n^{2} + 4967879197317800891547712786 n + 16413752167975604467326992340\right) a{\left(n + 18 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{2 \left(27978039856862695081734 n^{5} + 2429863358757344560529270 n^{4} + 83858149290807866857693735 n^{3} + 1441228765648819564284068385 n^{2} + 12392960231408872483541140246 n + 42986272735292463261569820480\right) a{\left(n + 21 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(29193813717116295330465 n^{5} + 3195593337199636201839332 n^{4} + 141643900957545775999758863 n^{3} + 3174859117091192016241305524 n^{2} + 35939235933213303919405624424 n + 164125029102820069468386822504\right) a{\left(n + 22 \right)}}{6 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{8 \left(53048284831600981113304 n^{5} + 4121109435346208406419650 n^{4} + 127916221239864533648639345 n^{3} + 1983081438638077597082865590 n^{2} + 15356297213723925330239419251 n + 47521050701271890166770661900\right) a{\left(n + 17 \right)}}{45 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(62059711014977137544669 n^{5} + 11742785546180915594427770 n^{4} + 887895859070762231214883375 n^{3} + 33535989249383379770976320050 n^{2} + 632755598670290906636407362936 n + 4771371867632995136405136791040\right) a{\left(n + 37 \right)}}{23040 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{2 \left(71053900839736908943601 n^{5} + 6172045704497552468879789 n^{4} + 214393182444893494679584189 n^{3} + 3723502527737613260924230171 n^{2} + 32342531603906191414235221074 n + 112436752745095427599269666696\right) a{\left(n + 19 \right)}}{9 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{2 \left(83126025286330979595819 n^{5} + 7419786639311891029531660 n^{4} + 264537662058945333968349650 n^{3} + 4711216339780844043779503605 n^{2} + 41935846232719720832358832346 n + 149371352181753212095533549480\right) a{\left(n + 20 \right)}}{15 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(93054059748275184757733 n^{5} + 15603588629730031872937865 n^{4} + 1044459373131591979395007060 n^{3} + 34880296428373788558749833900 n^{2} + 581050762836797590181075100672 n + 3861847476035461869552991062720\right) a{\left(n + 35 \right)}}{5760 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(585568881876520259640997 n^{5} + 98155211197154104044078235 n^{4} + 6578554121250693289891703870 n^{3} + 220363832171150054615598998120 n^{2} + 3689298958154950847306214619788 n + 24696292951364197176758805135840\right) a{\left(n + 34 \right)}}{5760 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(617583815509511667449699 n^{5} + 71680945458885932515162420 n^{4} + 3331940880935136103121680215 n^{3} + 77522738161837736904284820040 n^{2} + 902697570060791339259164660286 n + 4207961655009263586868549374480\right) a{\left(n + 23 \right)}}{30 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(1025859221166732942130183 n^{5} + 168382238429254427420197510 n^{4} + 11052836917372764334404056285 n^{3} + 362688221561869798914661858100 n^{2} + 5949472432545124135710854412612 n + 39030287826738030303224331833760\right) a{\left(n + 33 \right)}}{2880 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(1440636473196466680101426 n^{5} + 222964669347550327889425835 n^{4} + 13804784804808715144721778640 n^{3} + 427413668681344441347267996925 n^{2} + 6617514818647967203936301436369 n + 40988417891244282474921579785760\right) a{\left(n + 31 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(1781339502713891698880321 n^{5} + 284691149919752350813373440 n^{4} + 18198031397068496171506499545 n^{3} + 581582384796114780089704253650 n^{2} + 9292603382285472437424822720464 n + 59387568799038752672095931905200\right) a{\left(n + 32 \right)}}{1920 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(2275725347053487206470578 n^{5} + 324200318517546633861429935 n^{4} + 18481273301497905812137676458 n^{3} + 526988000598141867790050802465 n^{2} + 7516822353607995733983335694600 n + 42907748519651062100173771105224\right) a{\left(n + 29 \right)}}{288 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(3703522219585910581029506 n^{5} + 442834473059898301967097230 n^{4} + 21185688001360495828688652880 n^{3} + 506897567140961685124050884965 n^{2} + 6065491632069042034968090115359 n + 29037668627160399559640983937460\right) a{\left(n + 24 \right)}}{90 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(9097205967744551217048067 n^{5} + 1122422345341092993228731215 n^{4} + 55397740369173818236158497330 n^{3} + 1367181061362839061858148050215 n^{2} + 16871698529142712894138920556833 n + 83287683486898965261026741382300\right) a{\left(n + 25 \right)}}{180 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(11409385657778167984079114 n^{5} + 1559363769991214201924847125 n^{4} + 85262042685989833353356523325 n^{3} + 2331377684326115371127248334230 n^{2} + 31881083266477501552619727748626 n + 174430092274010765898041794739040\right) a{\left(n + 28 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(11410141747397456926932439 n^{5} + 1698169450629980046516175750 n^{4} + 101132763855553011023194315955 n^{3} + 3012596588015342511059616338600 n^{2} + 44888434386811841333499269286576 n + 267649991688270417800930195052240\right) a{\left(n + 30 \right)}}{2880 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} - \frac{\left(15770855530596627764168098 n^{5} + 2009746047769719080453446675 n^{4} + 102442474423747861933718212340 n^{3} + 2610880765640828669948872048655 n^{2} + 33271085653242490035754994814552 n + 169595554404051688596900395395320\right) a{\left(n + 26 \right)}}{360 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)} + \frac{\left(20888648906742153293876261 n^{5} + 2752614384077663580444980375 n^{4} + 145089670940710094238298964425 n^{3} + 3823874396752578258531031612855 n^{2} + 50391382540631383466508914051724 n + 265640117285438648956510837653600\right) a{\left(n + 27 \right)}}{720 \left(n + 52\right) \left(n + 53\right) \left(n + 55\right) \left(n + 56\right) \left(n + 58\right)}, \quad n \geq 56\)