A354674 a(n) = Sum_{k=0..n} k! * k^(k+n) * |Stirling1(n,k)|.

1, 1, 33, 4568, 1653010, 1236180194, 1657339714418, 3620923498508952, 12037504737979759944, 57827877567223173191712, 385581993722741959459382352, 3454851578510897594456017095504, 40509304222426523176427339597382336

Offset: 0

Author

Seiichi Manyama, Jun 02 2022

Keywords

• nonn

Crossrefs

Cf. A320096, A350721, A350722, A351333, A351769.

Programs

PARI

a(n) = sum(k=0, n, k!*k^(k+n)*abs(stirling(n, k, 1)));

PARI

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

Formula

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