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%I #10 Feb 15 2018 12:54:04
%S 2,4,302,8104,1189562,113466604,28069843622,6004208983504,
%T 2285772143562482,867405503682334804,478060568033873866142,
%U 280896639757518649936504,213833919524790465586194602
%N arctanh(tan(x)*sin(x))=2/2!*x^2+4/4!*x^4+302/6!*x^6+8104/8!*x^8...
%F a(n) ~ (2*n+1)! / (arctan(sqrt((1+sqrt(5))/2)))^(2*n+2). - _Vaclav Kotesovec_, Oct 24 2013
%t Table[n!*SeriesCoefficient[ArcTanh[Tan[x]*Sin[x]],{x,0,n}],{n,2,40,2}] (* _Vaclav Kotesovec_, Oct 24 2013 *)
%t With[{nn=30},Take[CoefficientList[Series[ArcTanh[Tan[x]Sin[x]],{x,0,nn}],x] Range[0,nn]!,{3,-1,2}]] (* _Harvey P. Dale_, Feb 15 2018 *)
%K nonn
%O 0,1
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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