OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (2*k+1)^(k-1) * binomial(n,2*k)/k!.
E.g.f.: sqrt(LambertW( -2*x^2/(1-x)^2 ) / (-2*x^2)).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^2)))/x))
(PARI) a(n) = n!*sum(k=0, n\2, (2*k+1)^(k-1)*binomial(n, 2*k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 03 2024
STATUS
approved