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 A276592 #35 Apr 01 2023 23:04:15
%S A276592 1,1,1,17,31,691,5461,929569,3202291,221930581,4722116521,56963745931,
%T A276592 14717667114151,2093660879252671,86125672563201181,
%U A276592 129848163681107301953,868320396104950823611,209390615747646519456961,14129659550745551130667441,16103843159579478297227731
%N A276592 Numerator of the rational part of the sum of reciprocals of even powers of odd numbers, i.e., Sum_{k>=1} 1/(2*k-1)^(2*n).
%C A276592 Apart from signs, same as A089171 and A279370. - _Peter Bala_, Feb 07 2019
%H A276592 Seiichi Manyama, <a href="/A276592/b276592.txt">Table of n, a(n) for n = 1..276</a>
%H A276592 Siddharth Dwivedi, Vivek Kumar Singh, and Abhishek Roy, <a href="https://arxiv.org/abs/2007.07033">Semiclassical limit of topological Rényi entropy in 3d Chern-Simons theory</a>, arXiv:2007.07033 [hep-th], 2020. See also <a href="https://doi.org/10.1007/JHEP12(2020)132">J. of High Energy Physics</a> (2020) Vol. 2020, Issue 12, Article 132.
%F A276592 a(n)/A276593(n) + A276594(n)/A276595(n) = A046988(n)/A002432(n).
%F A276592 a(n)/A276593(n) = (-1)^(n+1) * B_{2*n} * (2^(2*n) - 1) / (2 * (2*n)!), where B_n is the Bernoulli number. - _Seiichi Manyama_, Sep 03 2018
%p A276592 seq(numer(sum(1/(2*k-1)^(2*n),k=1..infinity)/Pi^(2*n)),n=1..22);
%t A276592 a[n_]:=Numerator[Pi^(-2 n) (1-2^(-2 n)) Zeta[2 n]] (* _Steven Foster Clark_, Mar 10 2023 *)
%t A276592 a[n_]:=Numerator[(-1)^n SeriesCoefficient[1/(E^x+1),{x,0,2 n-1}]] (* _Steven Foster Clark_, Mar 10 2023 *)
%t A276592 a[n_]:=Numerator[(-1)^n Residue[Zeta[s] Gamma[s] (1-2^(1-s)),{s,1-2 n}]] (* _Steven Foster Clark_, Mar 11 2023 *)
%Y A276592 Cf. A002432, A046988, A276593, A276594, A276595, A089171, A279370.
%K A276592 nonn,frac
%O A276592 1,4
%A A276592 _Martin Renner_, Sep 07 2016