A357662 Expansion of e.g.f. cosh( (exp(3*x) - 1)/sqrt(3) ).

1, 0, 3, 27, 198, 1485, 12825, 132678, 1582497, 20603727, 284290560, 4132840239, 63571690485, 1038868740000, 18022911716439, 330305863479615, 6355242571945878, 127721845479277737, 2672729031195365949, 58142565625982730462, 1313557910179640120061

Offset: 0

Author

Seiichi Manyama, Oct 07 2022

Keywords

• nonn

Crossrefs

Cf. A024430, A357661, A357663.

Cf. A357615, A357649, A357665.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\2, 3^(n-k)*stirling(n, 2*k, 2));

Formula

a(n) = Sum_{k=0..floor(n/2)} 3^(n-k) * Stirling2(n,2*k).