A350722 a(n) = Sum_{k=0..n} k! * k^(k+n) * Stirling2(n,k).

1, 1, 33, 4567, 1652493, 1235777551, 1656820330173, 3619858882041487, 12034209740498292093, 57813156798714532953391, 385490564193781368103929213, 3454086424032897924417605526607, 40500898779980258599522326286912893

Offset: 0

Author

Seiichi Manyama, Feb 03 2022

Keywords

• nonn

Crossrefs

Cf. A122399, A195005, A195263, A338040.

Cf. A108459, A350721, A351117.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k! * k^(k+n) * StirlingS2[n, k], {k, 1, n}]; Array[a, 13, 0] (* Amiram Eldar, Feb 03 2022 *)

PARI

a(n) = sum(k=0, n, k!*k^(k+n)*stirling(n, k, 2));

PARI

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

Formula

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

a(n) ~ exp(exp(-2)/2) * n! * n^(2*n). - Vaclav Kotesovec, Feb 04 2022