A381273 Expansion of e.g.f. exp(x * cosh(2*x)).

1, 1, 1, 13, 49, 201, 2161, 12629, 102817, 1118161, 9109921, 105660765, 1223720785, 13461561881, 186666204817, 2406325357861, 33607592404033, 516511765519521, 7658010172957249, 126206019752173997, 2115466479287184241, 36218229615683409001, 666810643855970901937

Offset: 0

Author

Seiichi Manyama, Feb 18 2025

Keywords

• sign

Comments

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

Crossrefs

Cf. A003727, A381274.

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, 2^(n-k)*a185951(n, k));

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).

a(n) = Sum_{k=0..n} 2^(n-k) * A185951(n,k).