OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: -LambertW(-x * exp(x^2/2)) / x = exp( x^2/2 - LambertW(-x*exp(x^2/2)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^(n-k-1) / (2^k * k! * (n-2*k)!).
a(n) ~ sqrt(1+LambertW(exp(-2))) * n^(n-1) / (exp(n)*LambertW(exp(-2))^((n+1)/2)). - Vaclav Kotesovec, Nov 10 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2/2-lambertw(-x*exp(x^2/2)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 02 2023
STATUS
approved