OFFSET
0,3
FORMULA
E.g.f.: exp( -LambertW((1 - exp(2*x))/2) ).
a(n) = Sum_{k=0..n} 2^(n-k) * (k+1)^(k-1) * Stirling2(n,k).
From Vaclav Kotesovec, Jul 18 2022: (Start)
E.g.f.: 2*LambertW((1 - exp(2*x))/2) / (1 - exp(2*x)).
a(n) ~ 2^(n - 1/2) * sqrt(exp(1) + 2) * n^(n-1) / (exp(n-1) * (log(exp(1) + 2) - 1)^(n - 1/2)). (End)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw((1-exp(2*x))/2))))
(PARI) a(n) = sum(k=0, n, 2^(n-k)*(k+1)^(k-1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 17 2022
STATUS
approved