A013522 Numerator of [x^(2n+1)] in the Taylor expansion sinh(cosec(x)-cotan(x))= x/2 +x^3/16 +37*x^5/3840 +137*x^7/92160 +41641*x^9/185794560 + 3887*x^11/117964800 +...

1, 1, 37, 137, 41641, 3887, 241586893, 5721418891, 4315903789009, 2832484672207, 183184249105857781, 2154299222076719401, 1431144441595717024523, 386845480523042818420133, 21349170171172632123182767, 38112676874301043070814698873, 25659732417088795005806537367241

Offset: 0

Author

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

Keywords

• nonn
• frac

Comments

Apparently a bisection of A047691.

The numerators in the e.g.f. of x/2, sinh(cosec(x)-cotan(x)) = x/(2^1*1!) +3*x^3/(2^3*3!) +37*x^5/(2^5*5!) +959*x^7/(2^7*7!) +41641*x^9/(2^9*9!)+.. are apparently covered by the absolute values of A003717.

Links

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

Programs

Mathematica

Numerator[Take[CoefficientList[Series[Sinh[Csc[x] - Cot[x]], {x,0,45}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 12 2016 *)

Extensions

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