A377532 Expansion of e.g.f. 1/(1 - x^2 * exp(x))^3.

1, 0, 6, 18, 180, 1500, 15930, 191646, 2580648, 38683224, 636068430, 11392350090, 220658360076, 4594593295188, 102333126352002, 2427278515815510, 61079333377870800, 1625065147997303856, 45576552142354413078, 1343802083242003570818, 41552482139458105525620

Offset

0,3

Links

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

Formula

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

a(n) ~ n! * n^2 / ((1 + LambertW(1/2))^3 * 2^(n+4) * LambertW(1/2)^n). - Vaclav Kotesovec, Oct 31 2024

Prog

(PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)*binomial(k+2, 2)/(n-2*k)!);

Crossrefs

Cf. A358080, A377531.

Sequence in context: A077531 A214537 A052634 * A059944 A052139 A354019

Adjacent sequences: A377529 A377530 A377531 * A377533 A377534 A377535

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 31 2024

Status

approved