A377681 Expansion of e.g.f. (1 + x * (exp(x) - 1))^4.

1, 0, 8, 12, 160, 740, 5424, 37828, 262784, 1868868, 13200880, 89816804, 581630592, 3586158628, 21162503600, 120273982980, 662169758464, 3549104142980, 18595278255600, 95559668680612, 482965743234560, 2405973280450404, 11835507260403376, 57577781030368196

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} k! * binomial(4,k) * Stirling2(n-k,k)/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n\2, k!*binomial(4, k)*stirling(n-k, k, 2)/(n-k)!);

Crossrefs

Cf. A377646, A377680.

Sequence in context: A067923 A258780 A228663 * A377684 A076028 A281256

Adjacent sequences: A377678 A377679 A377680 * A377682 A377683 A377684

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 04 2024

Status

approved