A351183 a(n) = Sum_{k=0..n} k^(2*n) * Stirling1(n,k).

1, 1, 15, 539, 28980, 1295404, -177715720, -88870557952, -11213754156480, 11072302541223336, 8352732988619491824, -1800044600955923261688, -8483589341410812834791040, -2945489916041839476122254560

Offset: 0

Author

Seiichi Manyama, Feb 04 2022

Keywords

• sign

Crossrefs

Cf. A229261, A320082, A351133, A351180, A351182.

Programs

PARI

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

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k^2*x)^k/k!)))

Formula

E.g.f.: Sum_{k>=0} log(1 + k^2*x)^k / k!.