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%I #14 Nov 21 2013 12:46:01
%S 0,1,2,4,0,-52,-440,-968,20160,407248,3393568,-7743232,-873283840,
%T -15700243392,-92423547008,3404251259008,126748437358592,
%U 1959254285705472,-9945595116842496,-1499843474292945920
%N arcsinh(arctanh(x)*exp(x))=x+2/2!*x^2+4/3!*x^3-52/5!*x^5-440/6!*x^6...
%F Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.451312658311... = abs(1/r), where r is the complex root of the equation exp(r)*log((1+r)/(1-r)) = -2*I. - _Vaclav Kotesovec_, Nov 02 2013
%t With[{nn=20},CoefficientList[Series[ArcSinh[ArcTanh[x]Exp[x]],{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Apr 05 2012, for right offset adapted by _Vaclav Kotesovec_, Nov 01 2013 *)
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Nov 01 2013
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