A380229 Expansion of e.g.f. exp( exp( (exp(3*x)-1)/3 ) - 1 ).

1, 1, 5, 32, 258, 2518, 28733, 374188, 5465748, 88364877, 1564525351, 30076618014, 623362069525, 13846300701886, 327952448024833, 8246654495001815, 219323630123687561, 6148716950721967215, 181171993247893669702, 5595764936875993028696, 180742802515427561158060, 6092097271225726649472555

Offset: 0

Author

Seiichi Manyama, Jan 17 2025

Keywords

• nonn

Crossrefs

Cf. A000258, A380228.

Cf. A369783.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(exp((exp(3*x)-1)/3)-1)))

Formula

a(n) = Sum_{k=0..n} 3^(n-k) * Stirling2(n,k) * Bell(k).