A009379 Expansion of log(1+tan(x)*x).

0, 2, -4, 96, -2080, 125440, -8629248, 996007936, -140162633728, 27058965184512, -6350990843576320, 1866805063173799936, -653569786506324738048, 273136898848234632380416, -133034893921204302732328960

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Crossrefs

Cf. A009399, A085984.

Programs

Mathematica

Log[ 1+Tan[ x ]*x ] (* Even Part *)
nn = 20; Table[(CoefficientList[Series[Log[1 + x*Tan[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 23 2015 *)

Formula

a(n) ~ (2*n)! * (-1)^(n+1) / (n * r^(2*n)), where r = 1.1996786402577338339163698486411419442614587884... (see A085984) is the root of the equation r*tanh(r) = 1. - Vaclav Kotesovec, Jan 23 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997