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%I #9 Feb 07 2015 05:35:43
%S 2,16,514,35152,4127746,740674064,188488949250,64571541708368,
%T 28651429011593218,15984853455121457680,10952019804412753091074,
%U 9040261830823734670831952,8848477099508752781113283586
%N tan(sinh(x)+sin(x))=2*x+16/3!*x^3+514/5!*x^5+35152/7!*x^7...
%H Vaclav Kotesovec, <a href="/A013028/b013028.txt">Table of n, a(n) for n = 0..200</a>
%H Vaclav Kotesovec, <a href="/A013028/a013028.jpg">Graph - abs(e.g.f.) in the complex plane</a>
%F a(n) ~ 2 * (2*n+1)! / ((cos(r) + cosh(r)) * r^(2*n+2)), where r = 0.782946098053298645157328067127669055159808275911641432279... is the root of the equation sinh(r) + sin(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015
%t nn = 20; Table[(CoefficientList[Series[Tan[Sin[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)