A013453 tan(tan(x)-tanh(x))=4/3!*x^3+544/7!*x^7+35840/9!*x^9+707584/11!*x^11...

0, 4, 0, 544, 35840, 707584, 298721280, 26768052224, 5564833464320, 1787224334270464, 379247341296680960, 181364573942845538304, 71776324876296729395200, 35085662010847230106271744

Offset: 0

Author

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

Keywords

• nonn

Programs

Mathematica

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 06 2015 *)

Formula

a(n) ~ 2 * (2*n+1)! / ((1/(cos(r))^2 - 1/(cosh(r))^2) * r^(2*n+2)), where r = 1.175536528296496445322181894766544798346231323714914157798... is the root of the equation tan(r)-tanh(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015

Extensions

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