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arctan(arctan(x)+tan(x))=2*x-16/3!*x^3+808/5!*x^5-99328/7!*x^7...
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%I #10 Nov 21 2013 12:46:01

%S 2,-16,808,-99328,22756480,-8373489408,4518380796928,

%T -3361577372366848,3297920024665948160,-4125214890387616169984,

%U 6407889739355365222383616,-12101572905129973895312965632

%N arctan(arctan(x)+tan(x))=2*x-16/3!*x^3+808/5!*x^5-99328/7!*x^7...

%t With[{nn=30},Take[CoefficientList[Series[ArcTan[ArcTan[x]+Tan[x]],{x,0,nn}], x]Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, May 05 2012 *)

%K sign

%O 0,1

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

%E Corrected definition - _N. J. A. Sloane_, Dec 17 2011