OFFSET
0,2
FORMULA
E.g.f.: exp( -LambertW(-2 * log(1+x)) ).
a(n) = Sum_{k=0..n} 2^k * (k+1)^(k-1) * Stirling1(n,k).
From Vaclav Kotesovec, Jul 17 2022: (Start)
E.g.f.: -LambertW(-2*log(1+x)) / (2*log(1+x)).
a(n) ~ sqrt(2) * n^(n-1) / ((exp(exp(-1)/2) - 1)^(n - 1/2) * exp(n - 3/2 + exp(-1)/4)). (End)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*log(1+x)))))
(PARI) a(n) = sum(k=0, n, 2^k*(k+1)^(k-1)*stirling(n, k, 1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 16 2022
STATUS
approved