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 18 2022: (Start)
E.g.f.: LambertW(2 * log(1-x)) / (2 * log(1-x)).
a(n) ~ sqrt(2) * n^(n-1) * exp(3/2 - n + n*exp(-1)/2) / (exp(exp(-1)/2) - 1)^(n - 1/2). (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)*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 16 2022
STATUS
approved