A013527 Numerator of [x^(2n)] of the Taylor expansion sec(cosec(x)-cot(x)) = 1+ x^2/8 +13*x^4/384 +397*x^6/46080 +4453*x^8/2064384 + ... .

1, 1, 13, 397, 4453, 24649, 12478897, 47378857957, 11289999097969, 1143069714638779, 1293273763150662781, 15203530875840895739, 46398798213229213203983, 209490216975221386279672393, 157153880464155360205476452597

Offset: 0

Author

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

Keywords

• nonn
• frac

Comments

The e.g.f. related to x/2, sec(cosec(x)-cot(x)) = 1 + 1*x^2/(2^2*2!) + 13*x^4/(2^4*4!) + 397*x^6/(2^6*6!) + 22265*x^8/(2^8*8!) + ..., is apparently provided by A009010.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..200

Programs

Mathematica

Numerator[Take[CoefficientList[Series[Sec[Csc[x] - Cot[x]], {x,0,50}], x], {1, -1, 2}]] (* G. C. Greubel, Nov 12 2016 *)

Extensions

Name edited by R. J. Mathar, Dec 20 2011