A377966 Expansion of e.g.f. (1+x)^2 * exp(x*(1+x)^3).

1, 3, 13, 85, 621, 5131, 48553, 500613, 5590105, 67453651, 868300581, 11854859413, 171122864773, 2598083998875, 41331779697601, 687151457132101, 11904595227392433, 214378528158055843, 4004773210169606845, 77459628036613435221, 1548502062887370346141

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n! * Sum_{k=0..n} binomial(3*k+2,n-k) / k!.

Prog

(PARI) a(n, s=2, t=3) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);

Crossrefs

Cf. A377954, A377965.

Cf. A361279, A377964, A377967.

Sequence in context: A152789 A192943 A366657 * A369550 A125500 A121679

Adjacent sequences: A377963 A377964 A377965 * A377967 A377968 A377969

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 12 2024

Status

approved