A375413 Expansion of e.g.f. exp(x^2 * (1 - x)^2) / (1 - x).

1, 1, 4, 0, 36, -60, 1920, -1680, 109200, -347760, 9858240, -27941760, 1321911360, -3675672000, 210819248640, -422918496000, 45482678841600, 432259027200, 11915705273472000, 32436011672064000, 3902063601673036800, 25891695005316940800, 1575143884245502771200

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

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

Crossrefs

Cf. A375410, A375415.

Sequence in context: A270159 A270213 A270184 * A271300 A271120 A174083

Adjacent sequences: A375410 A375411 A375412 * A375414 A375415 A375416

Keyword

sign

Author

Seiichi Manyama, Aug 14 2024

Status

approved