A012394 sec(tan(x)*tan(x))=1+12/4!*x^4+480/6!*x^6+32592/8!*x^8...

1, 0, 12, 480, 32592, 3644160, 601225152, 136477985280, 40777726478592, 15519265846026240, 7330634507726810112, 4208431377781384765440, 2886028889205733569318912, 2330210584650322816604897280

Offset: 0

Author

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

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200
• Vaclav Kotesovec, Graph - abs(e.g.f.) in the complex plane

Programs

Mathematica

nn = 20; Table[(CoefficientList[Series[Sec[Tan[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 08 2015 *)

Formula

a(n) ~ 2^(3/2) * (2*n)! / ((2+Pi) * sqrt(Pi) * (arctan(sqrt(Pi/2)))^(2*n+1)). - Vaclav Kotesovec, Feb 08 2015