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Numerator of the coefficient [x^(2n+1)] of the Taylor series arctanh(cosec(x) - coth(x)).
1

%I #18 Nov 15 2016 03:21:23

%S -1,13,29,397,74927,2570951,495301,2978520989,879781928617,

%T 1962442468445621,4485273725677799419,17810142018975186977

%N Numerator of the coefficient [x^(2n+1)] of the Taylor series arctanh(cosec(x) - coth(x)).

%H G. C. Greubel, <a href="/A013545/b013545.txt">Table of n, a(n) for n = 0..200</a> [Vincenzo Librandi computed the first 100 terms; Terms 101 to 200 computed by G. C. Greubel, Nov 13 2016]

%e -x/6 + 13*x^3/324 + 29*x^5/27216 + 397*x^7/2449440 + 74927*x^9/3491921664 + ... .

%t Numerator[Take[CoefficientList[Series[ArcTanh[Csc[x] - Coth[x]], {x, 0, 35}], x], {2, -2, 2}]] (* _Vincenzo Librandi_, Nov 12 2016 *)

%K sign,frac

%O 0,2

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

%E Name edited by _R. J. Mathar_, Dec 21 2011