A368767 a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * binomial(k+2,3) / k!).

1, 0, 4, 2, 28, 105, 686, 4718, 37864, 340611, 3406330, 37469344, 449632492, 5845221941, 81833107734, 1227496615330, 19639945846096, 333879079382663, 6009823428889074, 114186645148891076, 2283732902977823060, 47958390962534282489, 1055084601175754216782

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = n*a(n-1) + (-1)^n * binomial(n+2,3).

a(n) = n! + (-1)^n * A368585(n).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*sum(k=0, 2, binomial(2, k)*(-x)^k/(k+1)!)*exp(-x))/(1-x)))

Crossrefs

Cf. A368765, A368766, A368768.

Cf. A368585, A368763.

Sequence in context: A123670 A200032 A121667 * A291844 A353750 A093991

Adjacent sequences: A368764 A368765 A368766 * A368768 A368769 A368770

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2024

Status

approved