OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052880.
E.g.f.: exp( - 2*LambertW(1 - exp(x)) ).
a(n) = 2 * Sum_{k=0..n} (k+2)^(k-1) * Stirling2(n,k).
a(n) ~ 2*sqrt(exp(1) + 1) * n^(n-1) / (exp(n-2) * (log(exp(1) + 1)-1)^(n - 1/2)). - Vaclav Kotesovec, Sep 06 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-2*lambertw(1-exp(x)))))
(PARI) a(n) = 2*sum(k=0, n, (k+2)^(k-1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 01 2024
STATUS
approved