A380727 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^3 / (1 - x*A(x)^3)) / (1 - x*A(x)^3).

1, 2, 31, 988, 48533, 3240016, 274099723, 28110919712, 3389978711785, 470124480093184, 73718009095023191, 12897488652935429632, 2490884805057416903869, 526368104133213244928000, 120811269372167469194820547, 29928528196949304888405323776, 7959458742917430589011715194833

Offset: 0

Author

Seiichi Manyama, Jan 31 2025

Keywords

• nonn

Crossrefs

Cf. A380663, A380726.

Cf. A380724.

Programs

PARI

a(n) = n!*sum(k=0, n, (3*n+1)^(k-1)*binomial(4*n, n-k)/k!);

Formula

a(n) = n! * Sum_{k=0..n} (3*n+1)^(k-1) * binomial(4*n,n-k)/k!.