A356689 a(n) = n! * Sum_{k=0..n} k^(k*n)/k!.

1, 2, 20, 19887, 4297096180, 298028721722131825, 10314430386434427534836297166, 256923580889667624113335512704714686054849, 6277101737079381675512518990977258744796239498871290255000

Offset: 0

Author

Seiichi Manyama, Aug 23 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..26

Crossrefs

Cf. A256016, A356687, A356688.

Cf. A349886, A356674.

Programs

PARI

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

PARI

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

Formula

E.g.f.: Sum_{k>=0} (k^k * x)^k / (k! * (1 - k^k * x)).