A012753 - OEIS

%I #8 Feb 06 2015 10:49:16

%S 0,2,4,398,10344,1808442,161718060,45246852870,8895239749200,

%T 3696108480038130,1280274899653919700,747254995555318476030,

%U 400947704397371982315960,314940075899759001168711210

%N tan(arctanh(x)*arcsinh(x))=2/2!*x^2+4/4!*x^4+398/6!*x^6+10344/8!*x^8...

%F a(n) ~ 4 * (2*n)! / ((Pi / (arcsinh(r)*sqrt(1+r^2)) + 2*arcsinh(r) / (1-r^2)) * r^(2*n+1)), where r = 0.9521457236040528180035996172241256876113834258238... is the root of the equation arctanh(r)*arcsinh(r) = Pi/2. - _Vaclav Kotesovec_, Feb 06 2015

%t nn = 20; Table[(CoefficientList[Series[Tan[ArcSinh[x]*ArcTanh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Feb 06 2015 *)

%K nonn

%O 0,2

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

%E a(0)=0 prepended by _Vaclav Kotesovec_, Feb 06 2015