A013353 tan(tan(x)-sin(x)) = 3/3!*x^3 + 15/5!*x^5 + 273/7!*x^7 + 23055/9!*x^9...

0, 3, 15, 273, 23055, 1601193, 155341095, 24206437713, 4645592799135, 1094690215087833, 324803673636221175, 116133164181717551553, 48989776965837082135215, 24245825813770391843700873

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Vaclav Kotesovec, Graph - abs(e.g.f.) in the complex plane

Formula

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

Mathematica

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 *)

Crossrefs

Sequence in context: A013352 A013354 A013356 * A270401 A270001 A138896

Adjacent sequences: A013350 A013351 A013352 * A013354 A013355 A013356

Keyword

nonn

Author

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

Extensions

a(0)=0 prepended by Vaclav Kotesovec, Feb 06 2015

Definition modified by Vaclav Kotesovec, Feb 06 2015

Status

approved