A355469 Expansion of Sum_{k>=0} (k^3 * x/(1 - k^3 * x))^k.

1, 1, 65, 20708, 18383828, 34898769936, 121324513279512, 697408243146701056, 6165037130760825320768, 79390334273383043609851520, 1428007543233019703635181454080, 34693490969752778534655707874499584, 1107666867764009444258160579726602423808

Offset: 0

Author

Seiichi Manyama, Jul 03 2022

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..151

Crossrefs

Cf. A355468, A355470.

Programs

PARI

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

PARI

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

Formula

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