A380228 Expansion of e.g.f. exp( exp( (exp(2*x)-1)/2 ) - 1 ).

1, 1, 4, 21, 139, 1108, 10287, 108699, 1285228, 16783395, 239571125, 3706900992, 61746357449, 1100827515921, 20902202270580, 420903243601485, 8955301860908499, 200664408693149164, 4721693823656357303, 116370390417335016731, 2997078741899026174972, 80492590654279893652283

Offset: 0

Author

Seiichi Manyama, Jan 17 2025

Keywords

• nonn

Crossrefs

Cf. A000258, A380229.

Cf. A346417.

Programs

PARI

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

Formula

a(n) = Sum_{k=0..n} 2^(n-k) * Stirling2(n,k) * Bell(k).