A383053 a(n) = Sum_{k=0..n} (k+1)^4 * Stirling2(n,k).

1, 16, 97, 515, 2744, 15177, 88033, 536882, 3441439, 23151411, 163135410, 1201594675, 9232595661, 73858810120, 614045917741, 5296398334735, 47321198203496, 437310785441381, 4174403973827181, 41107555809612466, 417122543915965091, 4356601173778017487

Offset: 0

Author

Seiichi Manyama, Apr 14 2025

Keywords

• nonn

Comments

Stirling transform of (n+1)^4.

Links

• Eric Weisstein's World of Mathematics, Stirling Transform

Crossrefs

Cf. A000110, A222748, A362925.

Programs

PARI

a(n) = sum(k=0, n, (k+1)^4*stirling(n, k, 2));

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^4*(exp(x)-1)^k/k!)))

Formula

a(n) = A362925(n+4,4).

E.g.f.: Sum_{k>=0} (k+1)^4 * (exp(x) - 1)^k / k!.

E.g.f.: exp(exp(x) - 1) * Sum_{k=0..4} Stirling2(5,k+1) * (exp(x) - 1)^k.