%I #18 Dec 21 2017 17:28:06

%S 0,2,-4,96,-2080,125440,-8629248,996007936,-140162633728,

%T 27058965184512,-6350990843576320,1866805063173799936,

%U -653569786506324738048,273136898848234632380416,-133034893921204302732328960

%N Expansion of log(1+tan(x)*x).

%F 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

%t Log[ 1+Tan[ x ]*x ] (* Even Part *)

%t 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 *)

%Y Cf. A009399, A085984.

%K sign

%O 0,2

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997