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cos(arctan(x)*sin(x))=1-12/4!*x^4+360/6!*x^6-14000/8!*x^8...
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%I #6 May 24 2015 10:05:17

%S 1,0,-12,360,-14000,826560,-74707776,9918004096,-1826276458240,

%T 443565659817984,-136830226103770112,52123659256392435712,

%U -23992831220659002945536,13113491065080505366691840

%N cos(arctan(x)*sin(x))=1-12/4!*x^4+360/6!*x^6-14000/8!*x^8...

%t With[{nn=30},Take[CoefficientList[Series[Cos[ArcTan[x]Sin[x]],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, May 24 2015 *)

%K sign

%O 0,3

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