A012500 arctan(cos(x)*arctan(x))=x-7/3!*x^3+173/5!*x^5-11779/7!*x^7...

1, -7, 173, -11779, 1474969, -296068991, 87094091589, -35308668668155, 18872654969343537, -12860552599622997751, 10882609077370643446493, -11195876625633675125480947, 13761866805554489099492092361

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

E.g.f.: atan(cos(x)*atan(x)) = Sum_{n>=0} a(n)*x^(2*n+1)/(2*n+1)!.

Mathematica

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 *)

Prog

(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))

Crossrefs

Sequence in context: A332117 A226598 A075599 * A220326 A094257 A195887

Adjacent sequences: A012497 A012498 A012499 * A012501 A012502 A012503

Keyword

sign

Author

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

Extensions

Definition clarified by Harvey P. Dale, Oct 04 2015

Status

approved