A379990 Expansion of e.g.f. exp(-2*x)/(exp(-x) - x)^3.

1, 4, 25, 205, 2065, 24601, 337837, 5249581, 91006657, 1740663937, 36402220141, 826159146253, 20220201899377, 530828186303377, 14878044338021677, 443397290411503021, 14000282854007503105, 466866129420834410881, 16395362179348570608205, 604794784980600986425645

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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

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

Prog

(PARI) a(n) = n!*sum(k=0, n, (k+1)^(n-k)*binomial(k+2, 2)/(n-k)!);

Crossrefs

Cf. A377530, A379942, A379991.

Cf. A092148, A377529.

Sequence in context: A301363 A213192 A036242 * A120955 A061714 A005411

Adjacent sequences: A379987 A379988 A379989 * A379991 A379992 A379993

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 07 2025

Status

approved