A377967 Expansion of e.g.f. (1+x)^3 * exp(x*(1+x)^3).

1, 4, 19, 124, 961, 8236, 79339, 840484, 9595009, 117764596, 1542837091, 21406165804, 313381177729, 4822681240924, 77704955681851, 1307128152596116, 22899018541506049, 416756647023727204, 7863586717014612019, 153550319029835965276, 3097694623619639050561

Offset

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A361279, A377964, A377966.

Cf. A351767.

Sequence in context: A280939 A121125 A361240 * A099953 A009324 A203236

Adjacent sequences: A377964 A377965 A377966 * A377968 A377969 A377970

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 12 2024

Status

approved