OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..395
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * [x^n] exp(x + n*x^2).
E.g.f.: exp( sqrt( -LambertW(-2*x^2)/2 ) ) / (1 + LambertW(-2*x^2)).
a(n) ~ (1 + (-1)^n/exp(sqrt(2))) * 2^((n-1)/2) * n^n / exp(n/2 - 1/sqrt(2)). - Vaclav Kotesovec, Apr 15 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sqrt(-lambertw(-2*x^2)/2))/(1+lambertw(-2*x^2))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 14 2023
STATUS
approved