OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^(n-2*k-1) * binomial(n-k-1,k)/(n-2*k)!.
E.g.f.: exp( -LambertW(-x/(1-x^2)) ).
a(n) ~ (1 + 4*exp(-2))^(1/4) * 2^n * n^(n-1) / ((sqrt(1 + 4*exp(-2)) - 1)^n * exp(2*n-1)). - Vaclav Kotesovec, Sep 29 2024
PROG
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)^(n-2*k-1)*binomial(n-k-1, k)/(n-2*k)!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x^2)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 28 2024
STATUS
approved