OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: sqrt(LambertW( -2*x/(1-x)^2 ) / (-2*x)).
a(n) ~ sqrt(1 + 2*exp(-1) - sqrt(1 + 2*exp(-1))) * n^(n-1) / (2 * (sqrt(1 + 2*exp(-1)) - 1)^(3/2) * exp(2*n + 1/2) * (1 + exp(-1) - sqrt(1 + 2*exp(-1)))^n). - Vaclav Kotesovec, Mar 06 2023
a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(n+k,n-k)/k!. - Seiichi Manyama, Mar 09 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sqrt(lambertw(-2*x/(1-x)^2)/(-2*x))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 05 2023
STATUS
approved