A355496 Expansion of Sum_{k>=0} (k^3 * x/(1 - x))^k.

1, 1, 65, 19812, 16836458, 30584805344, 101712712528352, 559155681922806328, 4726278437746021089208, 58187531579876705928027712, 1000523517685151396828602120640, 23235157037192774575979788565151104, 709057406693306876515431403267191583808

Offset: 0

Author

Seiichi Manyama, Jul 04 2022

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..152

Crossrefs

Cf. A355494, A355495.

Cf. A355472, A355493.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x/(1-x))^k))

PARI

a(n) = if(n==0, 1, sum(k=1, n, k^(3*k)*binomial(n-1, k-1)));

Formula

a(n) = Sum_{k=1..n} k^(3*k) * binomial(n-1,k-1) for n > 0.