A377964 Expansion of e.g.f. (1+x) * exp(x*(1+x)^3).

1, 2, 9, 58, 389, 3186, 29437, 294554, 3233673, 38350594, 484794641, 6522118362, 92857444429, 1390937221298, 21858658599429, 359271578140666, 6156249977141777, 109722278546645634, 2029772196329985433, 38893956306343711994, 770622936760496106261, 15763542538016019828082

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A018191, A377963.

Cf. A361279, A377966, A377967.

Sequence in context: A124405 A300343 A141787 * A047852 A240881 A224127

Adjacent sequences: A377961 A377962 A377963 * A377965 A377966 A377967

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 12 2024

Status

approved