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arctan(sin(x)-arctan(x))=1/3!*x^3-23/5!*x^5+719/7!*x^7-40879/9!*x^9...
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%I #6 Nov 29 2016 10:54:59

%S 0,1,-23,719,-40879,3841319,-541803767,106235553423,-27468995761375,

%T 9037325540918231,-3685351559546907751,1824543182108925373567,

%U -1078031616167494916871951,749297439398817941026337799

%N arctan(sin(x)-arctan(x))=1/3!*x^3-23/5!*x^5+719/7!*x^7-40879/9!*x^9...

%t With[{nn=30},Take[CoefficientList[Series[ArcTanh[Sin[x]-ArcTan[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Ray Chandler_, Nov 29 2016 *)

%K sign

%O 0,3

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