A375425 Expansion of e.g.f. exp(-x * (1 - x)) / (1 - x)^3.

1, 2, 9, 44, 277, 1974, 16213, 148616, 1512201, 16872938, 205031041, 2694364452, 38080715869, 575998947614, 9284490424077, 158882422008704, 2876883685233553, 54953707187064786, 1104409466928407161, 23295036711306707228, 514558774836407746341

Offset: 0

Author

Seiichi Manyama, Aug 14 2024

Keywords

• nonn

Crossrefs

Cf. A375409, A375424.

Cf. A000153.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x))/(1-x)^3))

PARI

a(n) = (-1)^n*n!*sum(k=0, n, binomial(k-3, n-k)/k!);

Formula

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

a(n) = (n+1)*a(n-1) + 3*(n-1)*a(n-2) - 2*(n-1)*(n-2)*a(n-3).