OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..348
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp( -LambertW(-2*x * (1+x/2))/2 ).
a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (2*k+1)^(k-1) * binomial(k,n-k)/k!.
From Vaclav Kotesovec, Nov 10 2023: (Start)
E.g.f.: sqrt(-LambertW(-2*x * (1+x/2)) / (2*x * (1+x/2))).
a(n) ~ sqrt((-sqrt(1 + exp(-1)) + 1 + exp(-1))/2) * n^(n-1) / (exp(n-1) * (-1 + sqrt(1 + exp(-1)))^n). (End)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x*(1+x/2))/2)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 19 2023
STATUS
approved