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A362245 Expansion of e.g.f. 1/(1 - x * exp(x * (exp(x) - 1))). 4

%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

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Last modified March 2 10:43 EST 2024. Contains 370466 sequences. (Running on oeis4.)