OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..439
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: (-2 * LambertW(-x^2/2) / x^2)^(2/x) = exp(-2 * LambertW(-x^2/2) / x) = exp(x * exp(-LambertW(-x^2/2))).
a(n) = n! * Sum_{k=0..floor(n/2)} ((n-k)/2)^k * binomial(n-k-1,k)/(n-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^2/2)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 25 2023
STATUS
approved