A368587 a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+4,5) / k!.

0, 1, 4, 9, 20, 26, 96, -210, 2472, -20961, 211612, -2324729, 27901116, -362708320, 5077925048, -76168864092, 1218701840976, -20717931276243, 372922762998708, -7085532496941803, 141710649938878564, -2975923648716396714, 65470320271760793488

Offset

0,3

Links

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

Formula

a(0) = 0; a(n) = -n*a(n-1) + binomial(n+4,5).

E.g.f.: x * (1+2*x+x^2+x^3/6+x^4/120) * exp(x) / (1+x).

Prog

(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 4, binomial(4, k)*x^k/(k+1)!)*exp(x)/(1+x))))

Crossrefs

Cf. A009574, A368585, A368586.

Cf. A368576.

Sequence in context: A327238 A066109 A030734 * A212101 A073360 A297190

Adjacent sequences: A368584 A368585 A368586 * A368588 A368589 A368590

Keyword

sign,easy

Author

Seiichi Manyama, Dec 31 2023

Status

approved