A373708 Expansion of e.g.f. exp(x * (1 + x^4)^2).

1, 1, 1, 1, 1, 241, 1441, 5041, 13441, 393121, 10946881, 99902881, 559025281, 2335441681, 182348406241, 4382526067921, 48882114328321, 355837396998721, 5157802930734721, 312898934463543361, 7129755898022511361, 89524038506304371761, 773103613914955683361

Offset

0,6

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = n! * Sum_{k=0..floor(2*n/9)} binomial(2*n-8*k,k)/(n-4*k)!.

a(n) == 1 (mod 240).

a(n) = a(n-1) + 10*(n-1)*(n-2)*(n-3)*(n-4)*a(n-5) + 9*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*(n-7)*(n-8)*a(n-9).

Prog

(PARI) a(n) = n!*sum(k=0, 2*n\9, binomial(2*n-8*k, k)/(n-4*k)!);

Crossrefs

Cf. A361278, A373578, A373707.

Cf. A190877, A373524, A373525, A373526.

Cf. A373706.

Sequence in context: A159806 A142452 A167739 * A119596 A046948 A220056

Adjacent sequences: A373705 A373706 A373707 * A373709 A373710 A373711

Keyword

nonn

Author

Seiichi Manyama, Jun 14 2024

Status

approved