%I #9 Sep 08 2022 08:45:28

%S 1,2,12,102,1118,14936,234626,4227866,85826368,1935913962,47994717062,

%T 1296339943828,37870560693662,1189281013823922,39939332825682940,

%U 1427888927794137950,54132633478133801302,2168670060337770465208,91530447701766220582442

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

%H G. C. Greubel, <a href="/A123897/b123897.txt">Table of n, a(n) for n = 0..400</a>

%F a(n) ~ n^(n - 1/4) / ((1 + log(2))^(1/4) * log(1 + log(2))^(n + 1/4) * 2^(n/(1 + log(2)) - 2*sqrt(n)/((1 + log(2))^(3/2) * sqrt(log(1 + log(2)))) + 3/(2 + 2*log(2)) + 1/2) * exp(n/(1 + log(2)) - 2*sqrt(n)/((1 + log(2))^(3/2) * sqrt(log(1 + log(2)))) - (1/log(1 + log(2)) - 2)/(2*(1 + log(2))))). - _Vaclav Kotesovec_, Jun 26 2022

%p seq(coeff(series(exp(2*(exp(exp(x)-1)-1)/(2-exp(exp(x)-1))), x, n+1)*n!, x, n), n = 0 .. 20); # _G. C. Greubel_, Aug 06 2019

%t With[{m=20}, CoefficientList[Series[Exp[2*(Exp[Exp[x]-1]-1)/(2-Exp[Exp[x]-1])], {x,0,m}],x]*Range[0,m]!] (* _G. C. Greubel_, Aug 06 2019 *)

%o (PARI) my(x='x+O('x^20)); Vec(serlaplace( exp(2*(exp(exp(x)-1)-1)/(2-exp(exp(x)-1))) )) \\ _G. C. Greubel_, Aug 06 2019

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(2*(Exp(Exp(x)-1)-1)/(2-Exp(Exp(x)-1))) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 06 2019

%o (Sage) m = 20; T = taylor(exp(2*(exp(exp(x)-1)-1)/(2-exp(exp(x)-1))), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # _G. C. Greubel_, Aug 06 2019

%K nonn

%O 0,2

%A _Karol A. Penson_, Oct 18 2006

%E Terms a(16) onward added by _G. C. Greubel_, Aug 06 2019