A383054 a(n) = Sum_{k=0..n} (k+1)^5 * Stirling2(n,k).

1, 32, 275, 1785, 11002, 68303, 436297, 2891670, 19947717, 143327725, 1072207680, 8342947657, 67440657877, 565603592392, 4914839764895, 44191989524117, 410644596021954, 3938713285932859, 38950532224469117, 396712750010963782, 4157217331880368521

Offset: 0

Author

Seiichi Manyama, Apr 14 2025

Keywords

• nonn

Comments

Stirling transform of (n+1)^5.

Links

• Eric Weisstein's World of Mathematics, Stirling Transform

Crossrefs

Cf. A000110, A223023, A362925.

Programs

PARI

a(n) = sum(k=0, n, (k+1)^5*stirling(n, k, 2));

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^5*(exp(x)-1)^k/k!)))

Formula

a(n) = A362925(n+5,5).

E.g.f.: Sum_{k>=0} (k+1)^5 * (exp(x) - 1)^k / k!.

E.g.f.: exp(exp(x) - 1) * Sum_{k=0..5} Stirling2(6,k+1) * (exp(x) - 1)^k.