A373873 a(n) = Sum_{k=1..n} k! * k^(n-2) * Stirling2(n,k).

0, 1, 3, 31, 765, 34651, 2502213, 263824891, 38248036725, 7298877611371, 1773652375115973, 534749297993098651, 195883403209280580885, 85687658454617655817291, 44120264185381411695106533, 26413555571018242181844978811

Offset: 0

Author

Seiichi Manyama, Jun 20 2024

Keywords

• nonn

Crossrefs

Cf. A122399, A244585, A373871.

Cf. A220181, A373874, A373875.

Programs

Mathematica

Table[Sum[k! k^(n-2) StirlingS2[n,k],{k,n}],{n,0,20}] (* Harvey P. Dale, Jul 13 2025 *)

PARI

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

Formula

E.g.f.: Sum_{k>=1} (exp(k*x) - 1)^k / k^2.