A362245 Expansion of e.g.f. 1/(1 - x * exp(x * (exp(x) - 1))).
1, 1, 2, 12, 84, 680, 6750, 78372, 1035608, 15402816, 254672730, 4631221100, 91872810612, 1974481960464, 45698618329910, 1133221107064620, 29974735063385520, 842413032202481792, 25067919890384214066, 787394937539847359052, 26034146454319615550540
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x*(exp(x)-1)))))
Formula
a(n) = n! * Sum_{i=0..n} Sum_{j=0..n-i} i^j * Stirling2(n-i-j,j)/(n-i-j)!.
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