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%I #9 Feb 07 2015 04:29:23
%S 1,4,80,3176,240128,26523264,4329123968,926411177472,262606340440064,
%T 92031599216406528,40177149524079247360,20888461815920151461888,
%U 13005071730835628127846400,9394925108531366128729587712
%N tan(sec(x)*arcsinh(x))=x+4/3!*x^3+80/5!*x^5+3176/7!*x^7+240128/9!*x^9...
%H Vaclav Kotesovec, <a href="/A012824/b012824.txt">Table of n, a(n) for n = 0..200</a>
%H Vaclav Kotesovec, <a href="/A012824/a012824.jpg">Graph - abs(e.g.f.) in the complex plane</a>
%F a(n) ~ 4 * cos(r) * (2*n+1)! / ((2/sqrt(1+r^2) + Pi*sin(r)) * r^(2*n+2)), where r = 0.9838660479616109267190065546103701708288146085255331828633... is the root of the equation sec(r)*arcsinh(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015
%t nn = 20; Table[(CoefficientList[Series[Tan[ArcSinh[x]*Sec[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 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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