OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} (n-2*k+1)^(n-2*k-1) * binomial(n-2*k,k)/(n-2*k)!.
E.g.f.: exp( -LambertW(-x*(1+x^2)) ).
a(n) ~ sqrt(3 - 2*r*exp(1)) * n^(n-1) / (exp(n-1) * r^n), where r = 0.3314625163779096554724... is the real root of the equation r*(1 + r^2) = exp(-1). - Vaclav Kotesovec, Sep 29 2024
PROG
(PARI) a(n) = n!*sum(k=0, n\3, (n-2*k+1)^(n-2*k-1)*binomial(n-2*k, 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