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Expansion of tan(tan(x))*cos(x) (odd powers only).
0

%I #12 Jan 23 2015 14:26:50

%S 1,1,37,1517,108393,11820345,1828543693,380880450277,102776857839441,

%T 34874008165786609,14532999645144493557,7296638106447614270813,

%U 4344082656476890774001593,3025958669024832261385239593

%N Expansion of tan(tan(x))*cos(x) (odd powers only).

%F a(n) ~ (2*n-1)! * 16 / ((4+Pi^2)^(3/2) * arctan(Pi/2)^(2*n)). - _Vaclav Kotesovec_, Jan 23 2015

%t Tan[ Tan[ x ] ]*Cos[ x ] (* Odd Part *)

%t nn = 20; Table[(CoefficientList[Series[Cos[x]*Tan[Tan[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Jan 23 2015 *)

%K nonn

%O 1,3

%A _R. H. Hardin_

%E Extended and signs tested Mar 15 1997 by _Olivier GĂ©rard_.

%E Offset changed to 1 by _Vaclav Kotesovec_, Jan 23 2015