A012837 arctanh(sec(x)*tanh(x))=x+3/3!*x^3+65/5!*x^5+2723/7!*x^7...

1, 3, 65, 2723, 226785, 29857443, 5785047905, 1544546456963, 543833037679425, 244141035610073283, 136105726320473657345, 92251004006663786578403, 74707241586539626288837665

Offset

0,2

Links

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

Formula

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.825607669071161851569946033278187310658... is the root of the equation sec(r)*tanh(r) = 1. - Vaclav Kotesovec, Feb 05 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcTanh[Sec[x]*Tanh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 05 2015 *)

Crossrefs

Sequence in context: A346162 A012804 A348084 * A036778 A295169 A065400

Adjacent sequences: A012834 A012835 A012836 * A012838 A012839 A012840

Keyword

nonn

Author

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

Status

approved