A373742 Expansion of e.g.f. exp(x^3/6 * (1 + x)).

1, 0, 0, 1, 4, 0, 10, 140, 560, 280, 8400, 92400, 385000, 800800, 16816800, 169569400, 784784000, 3811808000, 68803134400, 673546473600, 3693641952000, 30454440016000, 507477434464000, 5002277568288000, 33870732912016000, 386622918281600000

Offset

0,5

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} binomial(k,n-3*k)/(6^k * k!).

a(n) = (n-1)*(n-2)/6 * (3*a(n-3) + 4*(n-3)*a(n-4)).

Prog

(PARI) a(n) = n!*sum(k=0, n\3, binomial(k, n-3*k)/(6^k*k!));

Crossrefs

Cf. A361568, A372743.

Cf. A017817.

Sequence in context: A279432 A019127 A019207 * A298449 A298056 A298706

Adjacent sequences: A373739 A373740 A373741 * A373743 A373744 A373745

Keyword

nonn

Author

Seiichi Manyama, Jun 16 2024

Status

approved