OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp( -LambertW(-x^2 / (1-x)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) * binomial(n-k-1,n-2*k)/k!.
a(n) ~ exp(1) * sqrt(1 + 4*exp(1) - sqrt(1 + 4*exp(1))) * 2^(n - 1/2) * n^(n-1) / ((1 + 2*exp(1) - sqrt(1 + 4*exp(1))) * (-1 + sqrt(1 + 4*exp(1)))^(n-1)). - Vaclav Kotesovec, Sep 26 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x^2/(1-x)))))
(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(n-k-1, n-2*k)/k!);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 26 2024
STATUS
approved