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 A164657 #19 Oct 07 2024 06:32:13
%S A164657 1,243,759375,12762815625,3101364196875,499477805270915625,
%T A164657 185452612752454075153125,185452612752454075153125,
%U A164657 263316190384861185784690603125,651996955695764397260286617707209375,651996955695764397260286617707209375,4196476041813743307955464949873473110315625
%N A164657 Denominators of partial sums of Theta(5) = Sum_{j>=1} 1/(2*j-1)^5.
%C A164657 The numerators are given by A164656.
%C A164657 For a reference and a W. Lang link see A164656.
%C A164657 Rationals (partial sums) Theta(5,n) := Sum_{j=1..n} 1/(2*j-1)^5 (in lowest terms). The limit of these rationals is Theta(5)= (1-1/2^5)*Zeta(5) approximately 1.004523763 (Zeta(n) is the Euler-Riemann zeta function).
%F A164657 a(n) = denominator(Theta(5,n)) = denominator(Sum_{j=1..n} 1/(2*j-1)^5).
%e A164657 Rationals Theta(5,n): [1, 244/243, 762743/759375, 12820180976/12762815625, 3115356499043/3101364196875,...].
%t A164657 r[n_] := Sum[1/(2*j-1)^5, {j, 1, n}]; (* or r[n_] := (PolyGamma[4, n+1/2] - PolyGamma[4, 1/2])/768 // FullSimplify; *) Table[r[n] // Denominator, {n, 1, 12}] (* _Jean-François Alcover_, Dec 02 2013 *)
%K A164657 nonn,frac,easy
%O A164657 1,2
%A A164657 _Wolfdieter Lang_, Oct 16 2009