A368585 a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+2,3) / k!.

0, 1, 2, 4, 4, 15, -34, 322, -2456, 22269, -222470, 2447456, -29369108, 381798859, -5345183466, 80177752670, -1282844041904, 21808348713337, -392550276838926, 7458455259940924, -149169105198816940, 3132551209175157511, -68916126601853463218

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+2,3).

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

Prog

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

Crossrefs

Cf. A009574, A368586, A368587.

Cf. A368574.

Sequence in context: A371254 A218974 A221706 * A145891 A077815 A218075

Adjacent sequences: A368582 A368583 A368584 * A368586 A368587 A368588

Keyword

sign,easy

Author

Seiichi Manyama, Dec 31 2023

Status

approved