A013523 Denominator of [x^(2n+1)] in the Taylor expansion arcsinh(cosec(x) - cot(x)).

2, 48, 768, 645120, 37158912, 81749606400, 784796221440, 42849873690624000, 548478383239987200, 63777066403145711616000, 4285818862291391820595200, 216862434431944426122117120000, 8007228348256409579893555200000, 1461479318123759876522171695104000000

Offset: 0

Author

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

Keywords

• nonn
• frac

Comments

Numerators are apparently covered by A091912.

The e.g.f. of x/2, arcsinh(cosec(x)-cot(x)) = x/(2^1*1!) + x^3/(2^3*3!) + 5*x^5/(2^5*5!) + 61*x^7/(2^7*7!) + 1385*x^9/(2^9*9!) + ... is apparently provided by the absolute values of A028296.

Examples

			x/2 + x^3/48 + x^5/768 + 61*x^7/645120 + 277*x^9/37158912 + ...
		

Links

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

Programs

Mathematica

Denominator[Take[CoefficientList[Series[ArcSinh[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