A377680 Expansion of e.g.f. (1 + x * (exp(x) - 1))^3.

1, 0, 6, 9, 84, 375, 1998, 11361, 60840, 299403, 1368930, 5906373, 24362748, 97019247, 375712470, 1422455625, 5286155088, 19340722707, 69831127242, 249265052301, 880927979940, 3086000399223, 10726216043070, 37020328044945, 126961071656184, 432900077950875

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} k! * binomial(3,k) * Stirling2(n-k,k)/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n\2, k!*binomial(3, k)*stirling(n-k, k, 2)/(n-k)!);

Crossrefs

Cf. A377646, A377681.

Cf. A375661.

Sequence in context: A204383 A266006 A372412 * A103107 A370623 A377683

Adjacent sequences: A377677 A377678 A377679 * A377681 A377682 A377683

Keyword

nonn,easy,new

Author

Seiichi Manyama, Nov 04 2024

Status

approved