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E.g.f.: arctanh(tan(x)+sin(x))=2*x+17/3!*x^3+865/5!*x^5+109007/7!*x^7...
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%I #8 Feb 05 2015 15:44:54

%S 2,17,865,109007,25619185,9676271447,5360201676505,4094035686738287,

%T 4123461735603625825,5295201587012317791527,8444330016251458512555145,

%U 16372171162004294836053543167

%N E.g.f.: arctanh(tan(x)+sin(x))=2*x+17/3!*x^3+865/5!*x^5+109007/7!*x^7...

%F a(n) ~ (2*n)! / (arctan((1-sqrt(2) + sqrt(2*sqrt(2)-1)) / (sqrt(2)-1 + sqrt(2*sqrt(2)-1))))^(2*n+1). - _Vaclav Kotesovec_, Feb 05 2015

%t With[{nn=30},Take[CoefficientList[Series[ArcTanh[Tan[x]+Sin[x]],{x,0,nn}],x]Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Jun 26 2012 *)

%K nonn

%O 0,1

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E Definition clarified by _Harvey P. Dale_, Jun 26 2012