OFFSET
0,3
FORMULA
a(n) = (n!/(n+1)) * Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(n+1,n-2*k)/(2^k * k!).
a(n) ~ (1 + 3*LambertW(1/3))^(n + 3/2) * n^(n-1) / (sqrt(1 + LambertW(1/3)) * 3^(3*n/2 + 2) * exp(n) * LambertW(1/3)^(3*(n+1)/2)). - Vaclav Kotesovec, Mar 06 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x*exp(x^2/2)))/x))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(n+1, n-2*k)/(2^k*k!))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 05 2024
STATUS
approved