%I #11 Aug 17 2018 22:32:49
%S 1,6,184,13360,1770880,373587200,115086003200,48784879769600,
%T 27245388132352000,19392357120188416000,17137521906875269120000,
%U 18411376349575875461120000,23632217190341837269237760000,35718167409293109428879360000000
%N arctanh(tan(arctanh(x))) = x + (6/3!)*x^3 + (184/5!)*x^5 + 13360/7!*x^7 + ...
%F a(n) ~ (2*n)! / (tanh(Pi/4))^(2*n+1). - _Vaclav Kotesovec_, Feb 05 2015
%p a:= n-> (t-> t!*coeff(series(arctanh(tan(arctanh(x))), x, t+1), x, t))(2*n+1):
%p seq(a(n), n=0..15); # _Alois P. Heinz_, Aug 17 2018
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[Tan[ArcTanh[x]]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)
%K nonn
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)