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

Author

Seiichi Manyama, Aug 21 2024

Keywords

• nonn

Crossrefs

Cf. A072597, A375395.

Programs

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!);

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