OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 21 2024
STATUS
approved