%I #10 Apr 13 2023 08:29:43
%S 1,1,2,12,84,680,6750,78372,1035608,15402816,254672730,4631221100,
%T 91872810612,1974481960464,45698618329910,1133221107064620,
%U 29974735063385520,842413032202481792,25067919890384214066,787394937539847359052,26034146454319615550540
%N Expansion of e.g.f. 1/(1 - x * exp(x * (exp(x) - 1))).
%F a(n) = n! * Sum_{i=0..n} Sum_{j=0..n-i} i^j * Stirling2(n-i-j,j)/(n-i-j)!.
%F a(n) ~ n! / ((1 - r + exp(r)*r*(1 + r)) * r^n), where r = 0.60489399462026660841486230237937164068755854932856922096976397761... is the root of the equation exp(r*(exp(r)-1)) = 1/r. - _Vaclav Kotesovec_, Apr 13 2023
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x*(exp(x)-1)))))
%Y Cf. A362244, A362246, A362247.
%Y Cf. A362238.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 12 2023