A368586 a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+3,4) / k!.

0, 1, 3, 6, 11, 15, 36, -42, 666, -5499, 55705, -611754, 7342413, -95449549, 1336296066, -20044437930, 320711010756, -5452087178007, 98137569210111, -1864613814984794, 37292276299704735, -783137802293788809, 17229031650463366448, -396267727960657413354

Offset

0,3

Links

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

Formula

a(0) = 0; a(n) = -n*a(n-1) + binomial(n+3,4).

E.g.f.: x * (1+3*x/2+x^2/2+x^3/24) * exp(x) / (1+x).

Prog

(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 3, binomial(3, k)*x^k/(k+1)!)*exp(x)/(1+x))))

Crossrefs

Cf. A009574, A368585, A368587.

Cf. A368575.

Sequence in context: A132158 A363644 A363652 * A310101 A310102 A310103

Adjacent sequences: A368583 A368584 A368585 * A368587 A368589 A368590

Keyword

sign,easy

Author

Seiichi Manyama, Dec 31 2023

Status

approved