A373743 Expansion of e.g.f. exp(x^3/6 * (1 + x)^2).

1, 0, 0, 1, 8, 20, 10, 280, 3360, 20440, 67200, 462000, 7407400, 73673600, 482081600, 3364761400, 47311264000, 657536880000, 6586994814400, 58707179731200, 740032028736000, 11832726841936000, 161121297104768000, 1857897194273120000, 23875495204536976000

Offset

0,5

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} binomial(2*k,n-3*k)/(6^k * k!).

a(n) = (n-1)*(n-2)/6 * (3*a(n-3) + 8*(n-3)*a(n-4) + 5*(n-3)*(n-4)*a(n-5)).

Prog

(PARI) a(n) = n!*sum(k=0, n\3, binomial(2*k, n-3*k)/(6^k*k!));

Crossrefs

Cf. A361568, A372742.

Cf. A361278, A361567.

Cf. A264622.

Sequence in context: A120081 A173206 A288423 * A081963 A208085 A334065

Adjacent sequences: A373740 A373741 A373742 * A373744 A373745 A373746

Keyword

nonn

Author

Seiichi Manyama, Jun 16 2024

Status

approved