A361547 Expansion of e.g.f. exp(x^5/(120 * (1-x))).

1, 0, 0, 0, 0, 1, 6, 42, 336, 3024, 30366, 335412, 4041576, 52756704, 741620880, 11169844686, 179448036768, 3063069801792, 55360031126400, 1056123043335360, 21208345049147256, 447183762148547424, 9877939209960101280, 228112734232663600320

Offset

0,7

Links

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

Formula

a(n) = 2*(n-1) * a(n-1) - (n-1)*(n-2) * a(n-2) + binomial(n-1,4) * a(n-5) - 4*binomial(n-1,5) * a(n-6) for n > 5.

From Seiichi Manyama, Jun 17 2024: (Start)

a(n) = n! * Sum_{k=0..floor(n/5)} binomial(n-4*k-1,n-5*k)/(120^k * k!).

a(0) = 1; a(n) = ((n-1)!/120) * Sum_{k=5..n} k * a(n-k)/(n-k)!. (End)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^5/(120*(1-x)))))

Crossrefs

Cf. A185369, A361533, A361545.

Sequence in context: A262671 A029588 A001725 * A123510 A265871 A132804

Adjacent sequences: A361544 A361545 A361546 * A361548 A361549 A361550

Keyword

nonn

Author

Seiichi Manyama, Mar 15 2023

Status

approved