A381274 Expansion of e.g.f. exp(x * cosh(3*x)).

1, 1, 1, 28, 109, 676, 10261, 65584, 881497, 11930896, 122708521, 2186539840, 30542901445, 477545743936, 9168255077437, 149358238356736, 3043023842477233, 61000460650291456, 1225825910880514129, 28395625697194028032, 621110654837608378141, 14936817377079335166976

Offset: 0

Author

Seiichi Manyama, Feb 18 2025

Keywords

• nonn

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Crossrefs

Cf. A003727, A381273.

Cf. A185951.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, 3^(n-k)*a185951(n, k));

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 9^k * (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).

a(n) = Sum_{k=0..n} 3^(n-k) * A185951(n,k).