This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A013524 #25 Aug 04 2024 04:15:19
%S A013524 1,0,-1,-1,-1,13,7951,21599,-294997,-275833,-60527057,-6338125867,
%T A013524 37620769159,10425684579701,5113538085001361,-25594556368763237,
%U A013524 -6013201989263028181,-3771502911169983097219,18335649295377317231411,669255665793644548301365603
%N A013524 Numerator of [x^(2n+1)] of the Taylor expansion tanh(cosec(x) - cot(x)).
%C A013524 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 A013524 G. C. Greubel, <a href="/A013524/b013524.txt">Table of n, a(n) for n = 0..200</a>
%F A013524 a(n) = numerator([x^(2*n+1)] tanh(tan(x/2))). - _Peter Luschny_, Nov 14 2016
%e A013524 Series starts: x/2 - x^5/480 - x^7/5760 - x^9/1451520 + 13*x^11/9676800 + 7951*x^13/49816166400 + ...
%p A013524 ser := series(tanh(tan(x/2)), x, 40):
%p A013524 seq(numer(coeff(ser, x, 2*n+1)), n=0..19); # _Peter Luschny_, Nov 14 2016
%t A013524 Numerator[Take[CoefficientList[Series[Tanh[Csc[x] - Cot[x]], {x,0,40}], x], {2, -1, 2}]] (* _G. C. Greubel_, Nov 12 2016 *)
%K A013524 sign,frac
%O A013524 0,6
%A A013524 Patrick Demichel (patrick.demichel(AT)hp.com)
%E A013524 Name edited by _R. J. Mathar_, Dec 19 2011