A357966 Expansion of e.g.f. exp( x * (exp(x^2) - 1) ).

1, 0, 0, 6, 0, 60, 360, 840, 20160, 75600, 1058400, 10311840, 79833600, 1305944640, 11018367360, 174616041600, 2150397849600, 28661419987200, 473667677683200, 6293779652160000, 114484773731328000, 1766543101087564800, 31640707215390873600

Offset: 0

Author

Seiichi Manyama, Oct 22 2022

Keywords

• nonn

Crossrefs

Cf. A357967, A357968.

Cf. A353226.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2)-1))))

PARI

a(n) = n!*sum(k=0, n\2, stirling(k, n-2*k, 2)/k!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} Stirling2(k,n-2*k)/k!.