A379995 Expansion of e.g.f. exp(-2*x)/(exp(-x) - x)^4.

1, 6, 48, 476, 5608, 76372, 1179016, 20332580, 387225120, 8068825988, 182564048824, 4456476380644, 116724944900272, 3264981100202564, 97130013288324552, 3062011655207131748, 101963095705628194624, 3576126056313566090500, 131762871920106615643480

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

a(n) ~ n! * n^3 / (6 * (LambertW(1) + 1)^4 * LambertW(1)^(n+2)). - Vaclav Kotesovec, Jan 08 2025

Prog

(PARI) a(n) = n!*sum(k=0, n, (k+2)^(n-k)*binomial(k+3, 3)/(n-k)!);

Crossrefs

Cf. A379943, A379993, A379994, A379996.

Cf. A358738.

Sequence in context: A319292 A261834 A226740 * A244509 A105627 A051578

Adjacent sequences: A379992 A379993 A379994 * A379996 A379997 A379998

Keyword

nonn,easy,new

Author

Seiichi Manyama, Jan 07 2025

Status

approved