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A013524 Numerator of [x^(2n+1)] of the Taylor expansion tanh(cosec(x) - cot(x)). 1

%I

%S 1,0,-1,-1,-1,13,7951,21599,-294997,-275833,-60527057,-6338125867,

%T 37620769159,10425684579701,5113538085001361,-25594556368763237,

%U -6013201989263028181,-3771502911169983097219,18335649295377317231411,669255665793644548301365603

%N Numerator of [x^(2n+1)] of the Taylor expansion tanh(cosec(x) - cot(x)).

%C The e.g.f. of x/2, tanh(cosec(x) - cot(x)) = x/(2^1*1!) - 8*x^5/(2^5*5!) - 112*x^7/(2^7*7!) - 128*x^9/(2^9*9!) + 109824*x^11/(2^11*11!) + ... is (up to signs) apparently provided by A003721.

%H G. C. Greubel, <a href="/A013524/b013524.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = numerator([x^(2*n+1)] tanh(tan(x/2)). - _Peter Luschny_, Nov 14 2016

%e Series starts: x/2 - x^5/480 - x^7/5760 - x^9/1451520 + 13*x^11/9676800 + 7951*x^13/49816166400 + ...

%p ser := series(tanh(tan(x/2)), x, 40):

%p seq(numer(coeff(ser, x, 2*n+1)), n=0..19); # _Peter Luschny_, Nov 14 2016

%t Numerator[Take[CoefficientList[Series[Tanh[Csc[x] - Cot[x]], {x,0,40}], x], {2, -1, 2}]] (* _G. C. Greubel_, Nov 12 2016 *)

%K sign,frac

%O 0,6

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

%E Name edited by _R. J. Mathar_, Dec 19 2011

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Last modified May 8 09:21 EDT 2021. Contains 343666 sequences. (Running on oeis4.)