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

0,2

Links

Table of n, a(n) for n=0..16.

Formula

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

Prog

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

Crossrefs

Cf. A380663, A380726.

Cf. A380724.

Sequence in context: A333349 A349071 A224863 * A379870 A263075 A217766

Adjacent sequences: A380724 A380725 A380726 * A380728 A380729 A380730

Keyword

nonn

Author

Seiichi Manyama, Jan 31 2025

Status

approved