A123898 - OEIS

%I #7 Sep 08 2022 08:45:28

%S 1,2,16,186,2822,52656,1163546,29664158,856061120,27560034858,

%T 978535914122,37963915297028,1597135176454118,72393848302855722,

%U 3516235184103738928,182148333985907278130,10022182002655953791542,583611259991958617165592,35852747516653556289308282

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

%H G. C. Greubel, <a href="/A123898/b123898.txt">Table of n, a(n) for n = 0..375</a>

%p seq(coeff(series(exp(2*(exp(exp(x/(1-x))-1)-1)/(2-exp(exp(x/(1-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-x)]-1]-1)/(2-Exp[Exp[x/(1-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-x))-1)-1)/(2-exp(exp(x/(1-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-x))-1)-1)/(2-Exp(Exp(x/(1-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-x))-1)-1)/(2-exp(exp(x/(1-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(17) onward added by _G. C. Greubel_, Aug 06 2019