A012741 - OEIS

%I #9 Feb 07 2015 03:32:23

%S 1,1,5,509,44393,4436441,630529965,126873147413,33552906028625,

%T 11170776120292657,4582643056340650197,2275243986686803354029,

%U 1344475182597566546716345,932197702028175163027746313

%N tan(arctanh(x)*cos(x))=x+1/3!*x^3+5/5!*x^5+509/7!*x^7+44393/9!*x^9...

%H Vaclav Kotesovec, <a href="/A012741/b012741.txt">Table of n, a(n) for n = 0..223</a>

%H Vaclav Kotesovec, <a href="/A012741/a012741.jpg">Graph - abs(e.g.f.) in the complex plane</a>

%F a(n) ~ 4 * (2*n+1)! / ((2*(cos(r)/(1-r^2)) - Pi*tan(r)) * r^(2*n+2)), where r = 0.993706174320375134478924859424390533447067228384145975655366... is the root of the equation arctanh(r)*cos(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015

%t nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[x]*Cos[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 0,3

%A Patrick Demichel (patrick.demichel(AT)hp.com)