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Expansion of e.g.f.: exp(exp(x)/sqrt(2-exp(2*x))-1).
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%I #14 Sep 08 2022 08:45:28

%S 1,2,12,112,1408,22144,417216,9148416,228649472,6412193280,

%T 199301663744,6798026395648,252397715738624,10131114555244544,

%U 437100940892913664,20169428831476678656,991081906535967948800,51662621871173444698112,2847287574653833612623872

%N Expansion of e.g.f.: exp(exp(x)/sqrt(2-exp(2*x))-1).

%C Exponential transform of A124212.

%H G. C. Greubel, <a href="/A124213/b124213.txt">Table of n, a(n) for n = 0..380</a>

%F E.g.f.: exp(exp(x)/sqrt(2-exp(2*x))-1).

%F a(n) ~ 2^(n + 1/6) * exp(3*n^(1/3)/(2^(2/3) * log(2)^(1/3)) - n - 1) * n^(n - 1/3) / (sqrt(3) * log(2)^(n + 1/6)). - _Vaclav Kotesovec_, Jun 26 2022

%t With[{nmax = 50}, CoefficientList[Series[Exp[Exp[x]/Sqrt[2 - Exp[2*x]] - 1], {x,0,nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Sep 27 2018 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(exp(x)/sqrt(2-exp(2*x))-1))) \\ _G. C. Greubel_, Sep 27 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(Exp(x)/Sqrt(2-Exp(2*x))-1))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Sep 27 2018

%Y Cf. A124212.

%K nonn

%O 0,2

%A _Karol A. Penson_, Oct 19 2006