A355470 Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - k^3 * x)^(k+1).

1, 1, 66, 21222, 18927560, 36030104000, 125486684755152, 722272396672485568, 6391048590559497227904, 82362961035803105954736768, 1482370265813455598541301007360, 36031982428595760278113744699088384, 1150873035676373345725887922070318410752

Offset: 0

Author

Seiichi Manyama, Jul 03 2022

Keywords

• nonn

Crossrefs

Cf. A355469, A355473.

Cf. A072034, A242446, A355466.

Programs

PARI

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

PARI

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

PARI

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

Formula

E.g.f.: Sum_{k>=0} exp(k^3 * x) * (k^3 * x)^k/k!.

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