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%I #13 May 20 2016 06:09:34
%S 1,1,13,677,54937,6248713,988579109,212756765101,60179200959793,
%T 21632158018229009,9619077100099258429,5182270736688171740085,
%U 3326876613520624630798281,2509818428217896837411045913,2198676694008933148388904662357,2213672191262297018716557756353725
%N arctanh(arctanh(x)*cos(x)) = x+1/3!*x^3+13/5!*x^5+677/7!*x^7+54937/9!*x^9...
%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.932706009172514... is the root of the equation cos(r)*log((1-r)/(1+r)) = -2. - _Vaclav Kotesovec_, Nov 02 2013
%t Table[n!*SeriesCoefficient[ArcTanh[ArcTanh[x]*Cos[x]],{x,0,n}],{n,1,41,2}] (* _Vaclav Kotesovec_, Nov 02 2013 *)
%t With[{nn=40},Take[CoefficientList[Series[ArcTanh[ArcTanh[x]Cos[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, May 20 2016 *)
%K nonn
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)