OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp( -LambertW(-x/(1-x)^2) ).
a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+k-1,n-k)/k!.
From Vaclav Kotesovec, Nov 10 2023: (Start)
E.g.f.: -LambertW(-x/(1-x)^2) * (1-x)^2 / x.
a(n) ~ 2^(n + 1/2) * sqrt(1 + 4*exp(-1) - sqrt(1 + 4*exp(-1))) * n^(n-1) / ((-1 + sqrt(1 + 4*exp(-1)))^(3/2) * (1 + 2*exp(-1) - sqrt(1 + 4*exp(-1)))^(n - 1/2) * exp(2*n-1)). (End)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^2))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 02 2023
STATUS
approved