A355493 Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - x)^(k+1).

1, 2, 67, 19879, 16856337, 30601661681, 101743314190033, 559257425236996361, 4726837695171258085569, 58192258417571877186113281, 1000581709943568968705788233921, 23236157618902718144948494353385025, 709080642850925779233576351761544968833

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. A086331, A323280.

Cf. A355470, A355473, A355496.

Programs

PARI

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

PARI

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

PARI

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

Formula

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

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