OFFSET
0,3
FORMULA
E.g.f.: exp( -LambertW(log(1-2*x)/2) ).
a(n) = Sum_{k=0..n} 2^(n-k) * (k+1)^(k-1) * |Stirling1(n,k)|.
From Vaclav Kotesovec, Jul 18 2022: (Start)
E.g.f.: 2*LambertW(log(1-2*x)/2) / log(1-2*x).
a(n) ~ 2^(n - 1/2) * n^(n-1) * exp(3/2 - n + 2*n*exp(-1)) / (exp(2*exp(-1)) - 1)^(n - 1/2). (End)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(log(1-2*x)/2))))
(PARI) a(n) = sum(k=0, n, 2^(n-k)*(k+1)^(k-1)*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 17 2022
STATUS
approved