A375394 Expansion of e.g.f. 1 / (exp(-x^2/2) - x).

1, 1, 3, 12, 63, 420, 3345, 31080, 330225, 3946320, 52401195, 765404640, 12196214415, 210533843520, 3913845680745, 77955813936000, 1656235524168225, 37387344753158400, 893615568162592275, 22545399132243187200, 598744483093370188575, 16696076277239091532800

Offset

0,3

Links

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

Formula

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

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / ((1 + LambertW(1)) * exp(n) * LambertW(1)^((n+1)/2)). - Vaclav Kotesovec, Aug 21 2024

Prog

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

Crossrefs

Cf. A072597, A375395.

Sequence in context: A355164 A373770 A238887 * A351778 A135889 A369746

Adjacent sequences: A375391 A375392 A375393 * A375395 A375396 A375397

Keyword

nonn

Author

Seiichi Manyama, Aug 21 2024

Status

approved