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

0,1

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.

Links

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

Example

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

Mathematica

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

Crossrefs

Sequence in context: A035606 A157057 A290690 * A260846 A009670 A024236

Adjacent sequences: A013520 A013521 A013522 * A013524 A013525 A013526

Keyword

nonn,frac

Author

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

Extensions

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

Status

approved