OFFSET
0,4
FORMULA
E.g.f.: exp( -LambertW((exp(-2*x) - 1)/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((exp(-2*x) - 1)/2) / (exp(-2*x) - 1).
a(n) ~ sqrt(exp(1)/2 - 1) * sqrt(-log(1 - 2*exp(-1))) * 2^n * n^(n-1) / (exp(n-1) * (1 - log(exp(1) - 2))^n). (End)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw((exp(-2*x)-1)/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