A381207 Expansion of e.g.f. 1/(1 - x*cosh(x))^3.

1, 3, 12, 69, 504, 4335, 43200, 490161, 6220032, 87242427, 1340305920, 22375475133, 403237638144, 7801208775399, 161245892161536, 3545854432602345, 82653484859228160, 2035605515838402291, 52814589875313573888, 1439814136866851346357, 41145786213980645621760

Offset: 0

Author

Seiichi Manyama, Feb 17 2025

Keywords

• nonn

Comments

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

Crossrefs

Cf. A377530, A381209, A381210, A381211.

Cf. A205571, A381206.

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, (k+2)!*a185951(n, k))/2;

Formula

a(n) = 1/2 * Sum_{k=0..n} (k+2)! * A185951(n,k).