A013519 Numerator of [x^(2n+1)] in the Taylor expansion tan(cosec(x)-cot(x)).

1, 1, 3, 181, 59, 3455, 3332389, 173339393, 449509681, 198232237033, 1032475444411, 101635950910031, 71432133543444211, 671713726985602398481

Offset: 0

Author

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

Keywords

• nonn
• frac

Comments

The e.g.f. of x/2, tan(cosec(x)-cot(x)) = x/(2^1*1!) + 4*x^3/(2^3*3!) +72*x^5/(2^5*5!) + 2896*x^7/(2^7*7!) +.. is apparently covered by A003718.

Examples

			x/2 +x^3/12 +3*x^5/160 +181*x^7/40320 +59*x^9/53760 +3455*x^11/12773376 +...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..125

Programs

Mathematica

Numerator[Take[CoefficientList[Series[Tan[Csc[x] - Cot[x]], {x, 0, 25}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 12 2016 *)

Extensions

Name edited by R. J. Mathar, Dec 19 2011