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 A360966 #29 Jun 11 2023 12:04:02
%S A360966 1,1,3,45,63,14175,93555,42567525,127702575,97692469875,371231385525,
%T A360966 2143861251406875,2275791174570375,48076088562799171875,
%U A360966 95646113035463615625,3952575621190533915703125,1441527579493018251609375,68739242628124575327993046875,333120945043988326589504765625
%N A360966 a(n) = denominator of (Zeta(2*n+1,1/4) - Zeta(2*n+1,3/4))/Pi^(2*n+1) where Zeta is the Hurwitz zeta function.
%C A360966 The function (Zeta(2*n+1,1/4) - Zeta(2*n+1,3/4))/Pi^(2*n+1) is rational for every positive integer n.
%C A360966 For numerators see A360945.
%H A360966 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a>
%F A360966 a(n) = A046983(2*n).
%F A360966 (Zeta(2*n + 1, 1/4) - Zeta(2*n + 1, 3/4))/(Pi^(2*n + 1)) = A000364(n)*(2*n + 1)*2^(2*n)/(2*n + 1)!.
%e A360966 a(0) = 1 because lim_{n->0} (Zeta(2*n+1,1/4) - Zeta(2*n+1,3/4))/Pi^(2*n+1) = 1.
%e A360966 a(3) = 45 because (Zeta(2*3+1,1/4) - Zeta(2*3+1,3/4))/Pi^(2*3+1) = 244/45.
%t A360966 Table[(Zeta[2*n + 1, 1/4] - Zeta[2*n + 1, 3/4]) / Pi^(2*n + 1), {n, 0, 25}] // FunctionExpand // Denominator
%t A360966 (* Second program: *)
%t A360966 a[n_] := SeriesCoefficient[Tan[x + Pi/4], {x, 0, 2n}] // Denominator;
%t A360966 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 16 2023 *)
%o A360966 (PARI) a(n) = denominator(abs(eulerfrac(2*n))*(2*n + 1)*2^(2*n)/(2*n + 1)!); \\ _Michel Marcus_, Apr 11 2023
%Y A360966 Bisection of A046983.
%Y A360966 Cf. A360945 (numerators).
%Y A360966 Cf. A000364, A046982, A173945, A173947, A173948, A173949, A173953, A173954, A173955, A173982, A173983, A173984, A173987, A361007.
%K A360966 nonn,frac
%O A360966 0,3
%A A360966 _Artur Jasinski_, Apr 09 2023