%I #11 Feb 06 2015 12:29:15

%S 0,3,15,273,23055,1601193,155341095,24206437713,4645592799135,

%T 1094690215087833,324803673636221175,116133164181717551553,

%U 48989776965837082135215,24245825813770391843700873

%N tan(tan(x)-sin(x)) = 3/3!*x^3 + 15/5!*x^5 + 273/7!*x^7 + 23055/9!*x^9...

%H Vaclav Kotesovec, <a href="/A013353/a013353.jpg">Graph - abs(e.g.f.) in the complex plane</a>

%F a(n) ~ 2 * (cos(r))^2 * (2*n+1)! / ((1-(cos(r))^3) * r^(2*n+2)), where r = 1.19018423208957072372902875764508033454996553596790725617361... is the root of the equation tan(r)-sin(r) = Pi/2. Also r = arcsin(t), where t = 0.928437423168555149184... is the root of the equation 4*t^4 + 4*Pi*t^3 + Pi^2*t^2 - 4*Pi*t - Pi^2 = 0. - _Vaclav Kotesovec_, Feb 06 2015

%t nn = 20; Table[(CoefficientList[Series[-Tan[Sin[x] - Tan[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 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

%E Definition modified by _Vaclav Kotesovec_, Feb 06 2015