A009702 Expansion of tan(tan(x))/cosh(x) (odd powers only).

1, 1, 57, 1657, 136977, 14004945, 2219125001, 457176874377, 123849671844513, 41945147421378337, 17490738249607542873, 8778749876346904238105, 5226971507061600220653233, 3640737476966979742943568113

Offset

1,3

Links

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

Formula

a(n) ~ (2*n-1)! * 8 / ((4+Pi^2) * cosh(arctan(Pi/2)) * arctan(Pi/2)^(2*n)). - Vaclav Kotesovec, Jan 23 2015

Mathematica

Tan[ Tan[ x ] ]/Cosh[ x ] (* Odd Part *)
nn = 20; Table[(CoefficientList[Series[Sech[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: A345457 A017773 A017720 * A282932 A228259 A229407

Adjacent sequences: A009699 A009700 A009701 * A009703 A009704 A009705

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