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 A091912 #27 Feb 16 2025 08:32:52
%S A091912 1,1,1,61,277,50521,41581,199360981,228135437,2404879675441,
%T A091912 14814847529501,69348874393137901,238685140977801337,
%U A091912 4087072509293123892361,454540704683713199807,441543893249023104553682821,2088463430347521052196056349
%N A091912 Numerators of Taylor series for log(tan(x)+1/cos(x)).
%C A091912 Absolute values of (reduced) numerators of Taylor series for the Gudermannian function gd(x)= 2*arctan(exp(x))-Pi/2. - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 28 2007
%D A091912 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 33, equations 33:14:14 - 33:14:15 at page 318.
%H A091912 Vincenzo Librandi, <a href="/A091912/b091912.txt">Table of n, a(n) for n = 0..100</a>
%H A091912 J. S. Robertson, <a href="http://www.jstor.org/stable/2687148">Gudermann and the Simple Pendulum</a>, The College Mathematics Journal, Vol. 28 (1997), No. 4, pp. 271-276.
%H A091912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Gudermannian.html">Gudermannian</a>.
%H A091912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/InverseGudermannian.html">Inverse Gudermannian</a>.
%F A091912 E.g.f.: sech(x) or gd(x). - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 28 2007
%e A091912 log(tan(x)+1/cos(x)) = x + 1/6*x^3 + 1/24*x^5 + 61/5040*x^7 + 277/72576*x^9 + ...
%e A091912 gd(x) = x - 1/6*x^3 + 1/24*x^5 - 61/5040*x^7 + 277/72576*x^9 + ....
%t A091912 Series[ArcTan[Sinh[x]], {x, 0, 30}] // CoefficientList[#, x]& // DeleteCases[#, 0]& // Numerator // Abs (* _Jean-François Alcover_, Feb 24 2014 *)
%t A091912 a[ n_] := (-1)^n Numerator @ SeriesCoefficient[ Gudermannian @ x, {x, 0, 2 n + 1}]; (* _Michael Somos_, Feb 24 2014 *)
%o A091912 (PARI) a(n)=local(X); if(n<0,0,X=x+O(x^(2*n+2)); numerator(polcoeff(log(tan(X)+1/cos(X)),2*n+1)))
%Y A091912 Cf. A000364, A028296.
%K A091912 nonn,frac,easy
%O A091912 0,4
%A A091912 _Michael Somos_, Feb 12 2004
%E A091912 More terms from _Vincenzo Librandi_, Feb 26 2014