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 A156769 #35 Oct 05 2024 16:30:12
%S A156769 1,3,15,315,2835,155925,6081075,638512875,10854718875,1856156927625,
%T A156769 194896477400625,49308808782358125,3698160658676859375,
%U A156769 1298054391195577640625,263505041412702261046875,122529844256906551386796875,4043484860477916195764296875
%N A156769 a(n) = denominator(2^(2*n-2)/factorial(2*n-1)).
%C A156769 Resembles A036279, the denominators in the Taylor series for tan(x). The first difference occurs at a(12).
%C A156769 The numerators of the two formulas for this sequence lead to A001316, Gould's sequence.
%C A156769 Stephen Crowley indicated on Aug 25 2008 that a(n) = denominator(Zeta(2*n)/Zeta(1-2*n)) and here numerator((Zeta(2*n)/Zeta(1-2*n))/(2*(-1)^(n)*(Pi)^(2*n))) leads to Gould's sequence.
%C A156769 This sequence appears in the Eta and Zeta triangles A160464 and A160474. Its resemblance to the sequence of the denominators of the Taylor series for tan(x) led to the conjecture A156769(n) = A036279(n)*A089170(n-1). - _Johannes W. Meijer_, May 24 2009
%H A156769 G. C. Greubel, <a href="/A156769/b156769.txt">Table of n, a(n) for n = 1..250</a>
%F A156769 a(n) = denominator( Product_{k=1..n-1} 2/(k*(2*k+1)) ).
%F A156769 G.f.: (1/2)*z^(1/2)*sinh(2*z^(1/2)).
%F A156769 From _Johannes W. Meijer_, May 24 2009: (Start)
%F A156769 a(n) = abs(A117972(n))/A000265(n).
%F A156769 a(n) = A036279(n)*A089170(n-1). (End)
%F A156769 a(n) = A049606(2*n-1). - _Zhujun Zhang_, May 29 2019
%p A156769 a := n ->(2*n-1)!*2^(add(i,i=convert(n-1,base,2))-2*n+2); # _Peter Luschny_, May 02 2009
%t A156769 a[n_] := Denominator[4^(n-1)/(2n-1)!];
%t A156769 Array[a, 15] (* _Jean-François Alcover_, Jun 20 2018 *)
%o A156769 (Magma) [Denominator(4^(n-1)/Factorial(2*n-1)): n in [1..25]]; // _G. C. Greubel_, Jun 19 2021
%o A156769 (Sage) [denominator(4^(n-1)/factorial(2*n-1)) for n in (1..25)] # _G. C. Greubel_, Jun 19 2021
%Y A156769 Cf. A036279 Denominators in Taylor series for tan(x).
%Y A156769 Cf. A001316 Gould's sequence appears in the numerators.
%Y A156769 Cf. A000265, A036279, A089170, A117972, A160464, A160469 (which resembles the numerators of the Taylor series for tan(x)), A160474. - _Johannes W. Meijer_, May 24 2009
%K A156769 easy,nonn
%O A156769 1,2
%A A156769 _Johannes W. Meijer_, Feb 15 2009