|
%I #9 May 08 2023 12:02:08
%S 1,0,0,6,12,20,1470,10122,47096,1814472,25119450,226527950,6732015972,
%T 142901684796,2071229736758,57596022404130,1589579741044080,
%U 32832196825559312,951335638952843826,31043287459520549910,838738470701197009820
%N Expansion of e.g.f. 1/(1 + LambertW(-x^2 * (exp(x) - 1))).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F a(n) = n! * Sum_{k=0..floor(n/3)} k^k * Stirling2(n-2*k,k)/(n-2*k)!.
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x^2*(exp(x)-1)))))
%Y Cf. A282190, A362836.
%Y Cf. A240989, A362891.
%K nonn
%O 0,4
%A _Seiichi Manyama_, May 08 2023
|
