A375427 Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x)^3.

1, 2, 11, 50, 349, 2314, 19903, 173354, 1796345, 19428146, 237268051, 3061371202, 43223040661, 646504620410, 10385505523079, 176415362111354, 3181608981134833, 60451307924295394, 1210235352100542235, 25421507156298185426, 559597201410003990221

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^2)/(1-x)^3))
(PARI) a(n) = (-1)^n*n!*sum(k=0, n, binomial(2*k-3, n-k)/k!);

Crossrefs

Cf. A375410, A375426.

Sequence in context: A357548 A137960 A018933 * A116586 A119366 A034574

Adjacent sequences: A375424 A375425 A375426 * A375428 A375429 A375430

Keyword

nonn

Author

Seiichi Manyama, Aug 14 2024

Status

approved