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arctan(arctan(x)+sin(x))=2*x-19/3!*x^3+1033/5!*x^5-139921/7!*x^7...
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%I #6 Apr 05 2016 11:59:52

%S 2,-19,1033,-139921,35331409,-14334032601,8528641989385,

%T -6996533376858481,7568756053179558689,-10439411395932267346985,

%U 17880910414730276822733721,-37235878792206753318991025025

%N arctan(arctan(x)+sin(x))=2*x-19/3!*x^3+1033/5!*x^5-139921/7!*x^7...

%t With[{nn=30},Take[CoefficientList[Series[ArcTan[ArcTan[x]+Sin[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Apr 05 2016 *)

%K sign

%O 0,1

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

%E Definition clarified by _Harvey P. Dale_, Apr 05 2016