A375409 Expansion of e.g.f. exp(-x * (1 - x)) / (1 - x).

1, 0, 3, 2, 33, 84, 835, 4542, 42273, 353672, 3670371, 39704730, 480066433, 6221189532, 87210179043, 1307488285334, 20923882733505, 355680675491472, 6402415875542083, 121644826003391922, 2432903816934178401, 51090929833475100260, 1124000813126981130243

Offset: 0

Author

Seiichi Manyama, Aug 14 2024

Keywords

• nonn

Crossrefs

Cf. A375410, A375411.

Cf. A375412, A375414.

Programs

PARI

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

PARI

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

Formula

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

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