A355373 a(n) = Sum_{k=0..n} k! * (-1)^k * n^(n-k) * Stirling2(n,k).

1, -1, 0, 3, 40, 455, 2016, -177373, -11564160, -497664081, -12796467200, 536297904659, 132025634657280, 14907422733429239, 1181852660381503488, 34684559693802943875, -11771644802057621110784, -3553614228958108389522721, -656899368126170250221715456

Offset: 0

Author

Seiichi Manyama, Jun 30 2022

Keywords

• sign

Crossrefs

Cf. A212846, A213127, A213128, A213129, A213130, A213131, A213132, A213133.

Cf. A318183, A352074.

Programs

Mathematica

a[n_] := Sum[k! * (-1)^k * n^(n - k) * StirlingS2[n, k], {k, 0, n}]; a[0] = 1; Array[a, 20, 0] (* Amiram Eldar, Jun 30 2022 *)

PARI

a(n) = sum(k=0, n, k!*(-1)^k*n^(n-k)*stirling(n, k, 2));

Formula

a(n) = n! * [x^n] n/(n - 1 + exp(n*x)) for n > 0.