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%I #9 Feb 07 2015 06:26:35
%S 2,16,544,40192,5111296,994586624,274584084480,102058445570048,
%T 49134745327894528,29743376752794664960,22111413979264501940224,
%U 19803614205698007369777152,21031646806008885489451401216
%N tan(tanh(x)+tan(x))=2*x+16/3!*x^3+544/5!*x^5+40192/7!*x^7...
%H Vaclav Kotesovec, <a href="/A013136/b013136.txt">Table of n, a(n) for n = 0..200</a>
%H Vaclav Kotesovec, <a href="/A013136/a013136.jpg">Graph - abs(e.g.f.) in the complex plane</a>
%F a(n) ~ 2 * (2*n+1)! / ((1/(cos(r))^2 + 1/(cosh(r))^2) * r^(2*n+2)), where r = 0.7516422408690037654862466685691510005314750319453074712524... is the root of the equation tanh(r) + tan(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015
%t nn = 20; Table[(CoefficientList[Series[Tan[Tan[x] + Tanh[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)
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