OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: LambertW( -x^2/(1-x) ) / (-x^2).
a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) * binomial(n-k,n-2*k)/k!.
a(n) ~ exp(2) * sqrt(1 + 4*exp(1) - sqrt(1 + 4*exp(1))) * 2^(n + 3/2) * n^(n-1) / ((1 + 2*exp(1) - sqrt(1 + 4*exp(1)))*(-1 + sqrt(1 + 4*exp(1)))^(n+1)). - Vaclav Kotesovec, Mar 12 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(-x^2/(1-x))/(-x^2)))
(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(n-k, n-2*k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 09 2024
STATUS
approved