A013521 Numerator of [x^(2n)] in the Taylor expansion cos(cosec(x)-cot(x))= 1-x^2/8 -7*x^4/384 -97*x^6/46080 -2063*x^8/10321920 -17803*x^10/1238630400 -....

1, -1, -7, -97, -2063, -17803, -250781, 166831871, 43685848289, 447550424579, 84677077231169, 11657476758734011, 28924058075775365981, 44287070229737735633567, 305190813989360271816409

Offset: 0

Author

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

Keywords

• sign
• frac

Comments

The e.g.f of x/2, cos(cosec(x)-cot(x)) = 1 -1*x^2/(2^2*2!) -7*x^4/(2^4*4!) -97*x^6/(2^6*6!) -2063*x^8/(2^8*8!) -..., is apparently covered by A003710.

Links

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

Programs

Mathematica

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

Extensions

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