A385309 Expansion of e.g.f. 1/(1 - 3 * x * cosh(x))^(1/3).

1, 1, 4, 31, 328, 4485, 75520, 1509347, 34916224, 917703145, 27011107840, 880133628231, 31451749424128, 1223047891889837, 51414400611438592, 2323391075748100555, 112315439676217262080, 5783449255108473820497, 316034972288791445241856, 18265740423344520141491951

Offset: 0

Author

Seiichi Manyama, Jun 24 2025

Keywords

• nonn

Crossrefs

Cf. A205571, A385308.

Cf. A380017, A385305, A385307, A385311.

Cf. A007559, A185951, A352649, A385282.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k)*a185951(n, k));

Formula

a(n) = Sum_{k=0..n} A007559(k) * A185951(n,k), where A185951(n,0) = 0^n.