A355466 Expansion of Sum_{k>=0} (k^k * x)^k/(1 - k^k * x)^(k+1).

1, 2, 19, 19879, 4297094601, 298028721578591321, 10314430386430205371442173873, 256923580889667562995278943476559835493321, 6277101737079381674883855772624745947410338680458857322625

Offset: 0

Author

Seiichi Manyama, Jul 03 2022

Keywords

• nonn

Crossrefs

Cf. A072034, A242446, A355470.

Cf. A349886.

Programs

PARI

my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, (k^k*x)^k/(1-k^k*x)^(k+1)))

PARI

my(N=10, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, exp(k^k*x)*(k^k*x)^k/k!)))

PARI

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

Formula

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

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