A009695 Expansion of tan(tan(x))*cos(x) (odd powers only).

1, 1, 37, 1517, 108393, 11820345, 1828543693, 380880450277, 102776857839441, 34874008165786609, 14532999645144493557, 7296638106447614270813, 4344082656476890774001593, 3025958669024832261385239593

Offset

1,3

Links

Table of n, a(n) for n=1..14.

Formula

a(n) ~ (2*n-1)! * 16 / ((4+Pi^2)^(3/2) * arctan(Pi/2)^(2*n)). - Vaclav Kotesovec, Jan 23 2015

Mathematica

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

Crossrefs

Sequence in context: A094490 A231543 A279330 * A201956 A322097 A383632

Adjacent sequences: A009692 A009693 A009694 * A009696 A009697 A009698

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

Offset changed to 1 by Vaclav Kotesovec, Jan 23 2015

Status

approved