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%I #7 Oct 04 2015 13:06:34
%S 1,-7,173,-11779,1474969,-296068991,87094091589,-35308668668155,
%T 18872654969343537,-12860552599622997751,10882609077370643446493,
%U -11195876625633675125480947,13761866805554489099492092361
%N arctan(cos(x)*arctan(x))=x-7/3!*x^3+173/5!*x^5-11779/7!*x^7...
%F E.g.f.: atan(cos(x)*atan(x)) = Sum_{n>=0} a(n)*x^(2*n+1)/(2*n+1)!.
%t With[{nn=30},Take[CoefficientList[Series[ArcTan[Cos[x]ArcTan[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Oct 04 2015 *)
%o (PARI) a(n)=local(y); if(n<0,0,y=x+x^2*O(x^(2*n)); (2*n+1)!*polcoeff(atan(cos(y)*atan(y)),2*n+1))
%K sign
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Definition clarified by _Harvey P. Dale_, Oct 04 2015
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