A365843
Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1+x)^3 ).
Original entry on oeis.org
1, 6, 54, 578, 6810, 85278, 1113854, 15004746, 206955378, 2908113974, 41484917958, 599202514578, 8745727050762, 128790559374030, 1911191826600462, 28551332345784730, 429040549473424866, 6480799118506040934, 98349636147075506006, 1498732955394826784226
Offset: 0
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a(n) = sum(k=0, n, binomial(3*n+k+2, k)*binomial(3*(n+1), n-k))/(n+1);
A370097
a(n) = Sum_{k=0..n} binomial(3*n,k) * binomial(3*n-k-1,n-k).
Original entry on oeis.org
1, 5, 49, 545, 6401, 77505, 956929, 11976193, 151388161, 1928363009, 24712450049, 318255628289, 4115300220929, 53396370030593, 694845537386497, 9064787191660545, 118516719269445633, 1552528215946035201, 20372392543502991361, 267736366910401413121
Offset: 0
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Table[Sum[2^k*(-1)^(n-k)*Binomial[3*n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 31 2025 *)
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a(n) = sum(k=0, n, binomial(3*n, k)*binomial(3*n-k-1, n-k));
A365844
Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1+x)^3 ).
Original entry on oeis.org
1, 7, 74, 931, 12894, 189798, 2913980, 46140347, 748022678, 12354604274, 207148525484, 3516699607022, 60328735646620, 1044182053141612, 18212018061261600, 319771572646888811, 5647677332549552870, 100266714048150595770, 1788366334642393259292
Offset: 0
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a(n) = sum(k=0, n, binomial(4*n+k+3, k)*binomial(3*(n+1), n-k))/(n+1);
A365845
Expansion of (1/x) * Series_Reversion( x*(1-x)^5/(1+x)^3 ).
Original entry on oeis.org
1, 8, 97, 1400, 22243, 375584, 6614508, 120136984, 2234022775, 42322629960, 813939319697, 15849232257824, 311858145053076, 6191083938051840, 123852349440862504, 2494251111318893400, 50526944132627936127, 1028872756710478785560
Offset: 0
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a(n) = sum(k=0, n, binomial(5*n+k+4, k)*binomial(3*(n+1), n-k))/(n+1);
Showing 1-4 of 4 results.