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 A053005 #23 May 30 2025 11:01:54
%S A053005 4,32,1536,184320,8257536,14863564800,1569592442880,5713316492083200,
%T A053005 1096956766479974400,6713375410857443328000,408173224980132554342400,
%U A053005 18857602994082124010618880000,640578267860512766391484416000
%N A053005 Denominator of beta(2n+1)/Pi^(2n+1), where beta(m) = Sum_{k=0..inf} (-1)^k/(2k+1)^m.
%D A053005 J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 384, Problem 15.
%D A053005 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Problem 37, beta(n).
%H A053005 T. D. Noe, <a href="/A053005/b053005.txt">Table of n, a(n) for n = 0..100</a>
%H A053005 Jan W. H. Swanepoel, <a href="https://math.colgate.edu/~integers/z50/z50.pdf">A Short Simple Probabilistic Proof of a Well Known Identity and the Derivation of Related New Identities Involving the Bernoulli Numbers and the Euler Numbers</a>, Integers (2025) Vol. 25, Art. No. A50. See p. 4.
%H A053005 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletBetaFunction.html">Dirichlet Beta Function</a>
%e A053005 beta(5) = 5*Pi^5/1536 so a(2)=1536.
%t A053005 beta[1] = Pi/4; beta[m_] := (Zeta[m, 1/4] - Zeta[m, 3/4])/4^m; a[n_, p_] := a[n, p] = beta[2*n+1]/Pi^(2*n+1) // N[#, p]& // Rationalize[#, 0]& // Denominator; a[n_] := Module[{p = 16}, a[n, p]; p = 2*p; While[a[n, p] != a[n, p/2], p = 2*p]; a[n, p]]; Table[a[n], {n, 0, 13}] (* _Jean-François Alcover_, Aug 19 2013 *)
%Y A053005 Cf. A046976.
%K A053005 nonn,frac,nice,easy
%O A053005 0,1
%A A053005 _N. J. A. Sloane_, Feb 21 2000