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%I #15 Sep 08 2022 08:45:28
%S 1,2,10,70,626,6774,85714,1238710,20096146,361205046,7118099922,
%T 152499926198,3527182848786,87554148952118,2320744552177234,
%U 65401560669438902,1952122937140314002,61507654345360320310,2039679556472462415570,70998682644763584004790
%N Expansion of e.g.f.: exp( 2*(exp(x)-1)/(2-exp(x)) ).
%H G. C. Greubel, <a href="/A123881/b123881.txt">Table of n, a(n) for n = 0..415</a>
%F a(n) ~ n^(n-1/4) * exp(2*sqrt(n)/sqrt(log(2)) - n + 1/(2*log(2)) - 3/2) / (sqrt(2)*log(2)^(n+1/4)). - _Vaclav Kotesovec_, Jun 03 2013
%p seq(coeff(series(exp( 2*(exp(x)-1)/(2-exp(x)) ), x, n+1)*factorial(n), x, n), n = 0..20); # _G. C. Greubel_, Aug 08 2019
%t CoefficientList[Series[E^(2*(E^x-1)/(2-E^x)), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 03 2013 *)
%t Table[Sum[BellY[n, k, PolyLog[-Range[n], 1/2]], {k, 0, n}], {n, 0, 20}] (* _Vladimir Reshetnikov_, Nov 09 2016 *)
%o (PARI) my(x='x+O('x^20)); Vec(serlaplace( exp( 2*(exp(x)-1)/(2-exp(x)) ) )) \\ _G. C. Greubel_, Aug 08 2019
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp( 2*(Exp(x)-1)/(2-Exp(x)) ) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 08 2019
%o (Sage) m = 20; T = taylor(exp( 2*(exp(x)-1)/(2-exp(x)) ), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # _G. C. Greubel_, Aug 08 2019
%K nonn
%O 0,2
%A _Karol A. Penson_, Oct 16 2006
%E Terms a(17) onward added by _G. C. Greubel_, Aug 08 2019
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