A373707 Expansion of e.g.f. exp(x * (1 + x^3)^2).

1, 1, 1, 1, 49, 241, 721, 6721, 124321, 913249, 4243681, 94818241, 1640604241, 14642181841, 131026944049, 3669304504321, 62536989802561, 627395160826561, 10818406189690561, 308036857749752449, 5219006583104930161, 65146235714284117681

Offset

0,5

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * Sum_{k=0..floor(2*n/7)} binomial(2*n-6*k,k)/(n-3*k)!.

a(n) == 1 (mod 48).

a(n) = a(n-1) + 8*(n-1)*(n-2)*(n-3)*a(n-4) + 7*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*a(n-7).

Prog

(PARI) a(n) = n!*sum(k=0, 2*n\7, binomial(2*n-6*k, k)/(n-3*k)!);

Crossrefs

Cf. A361278, A373578, A373708.

Cf. A190875, A373522, A373523.

Cf. A373680.

Sequence in context: A266799 A211741 A211761 * A373680 A322675 A260198

Adjacent sequences: A373704 A373705 A373706 * A373708 A373709 A373710

Keyword

nonn

Author

Seiichi Manyama, Jun 14 2024

Status

approved