A012726 - OEIS

%I #10 Feb 05 2015 09:47:33

%S 0,2,16,560,39296,4768768,881315840,230827284480,81324940394496,

%T 37097190468747264,21272100905987080192,14977571327515946909696,

%U 12703902924309766749552640,12776509288228175937154318336

%N arctanh(arctanh(x)*tan(x))=2/2!*x^2+16/4!*x^4+560/6!*x^6+39296/8!*x^8...

%F a(n) ~ (2*n-1)! / r^(2*n), where r = 0.772419882704426062944736631601064953563... is the root of the equation arctanh(r)*tan(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015

%t With[{nn=30},Flatten[{0,Take[CoefficientList[Series[ArcTanh[ArcTanh[x]Tan[x]],{x,0,nn}],x] Range[0,nn]!,{3,-1,2}]}]] (* _Harvey P. Dale_, Aug 26 2014 *)

%K nonn

%O 0,2

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

%E Definition clarified by _Harvey P. Dale_, Aug 26 2014

%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Feb 05 2015