A375426 Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x)^2.

1, 1, 7, 17, 149, 569, 6019, 34033, 409513, 3261041, 42986591, 451422641, 6486586237, 84605091817, 1334440837339, 20632779265169, 358963187353169, 6363955245003233, 122111809463225143, 2427035466387882961, 51167058284040281701, 1122982719058921672601

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A375410, A375427.

Sequence in context: A244279 A364703 A325584 * A214149 A147643 A367809

Adjacent sequences: A375423 A375424 A375425 * A375427 A375428 A375429

Keyword

nonn

Author

Seiichi Manyama, Aug 14 2024

Status

approved