OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..427
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: (-LambertW(-x^3) / x^3)^(1/x^2) = exp(-LambertW(-x^3) / x^2) = exp(x * exp(-LambertW(-x^3))).
a(n) = n! * Sum_{k=0..floor(n/3)} (n-2*k)^k * binomial(n-2*k-1,k)/(n-2*k)!.
E.g.f.: Sum_{k>=0} (k*x^2 + 1)^(k-1) * x^k / k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-lambertw(-x^3)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 25 2023
STATUS
approved