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%I #8 Feb 07 2015 05:45:07
%S 2,18,682,55762,7861330,1695960882,519152347066,213968420883442,
%T 114231299480266658,76681416778961132498,63215479683812222209738,
%U 62785613460405843207533202,73943247063260517632498040818
%N tan(sinh(x)+arcsin(x))=2*x+18/3!*x^3+682/5!*x^5+55762/7!*x^7...
%H Vaclav Kotesovec, <a href="/A013035/b013035.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ 2 * (2*n+1)! / ((1/sqrt(1-r^2) + cosh(r)) * r^(2*n+2)), where r = 0.7137663392321306757068472447735817625797877657851167410885... is the root of the equation sinh(r) + arcsin(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015
%t nn = 20; Table[(CoefficientList[Series[Tan[ArcSin[x] + Sinh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 07 2015 *)
%K nonn
%O 0,1
%A Patrick Demichel (patrick.demichel(AT)hp.com)