OFFSET
1,4
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..276
Siddharth Dwivedi, Vivek Kumar Singh, and Abhishek Roy, Semiclassical limit of topological Rényi entropy in 3d Chern-Simons theory, arXiv:2007.07033 [hep-th], 2020. See also J. of High Energy Physics (2020) Vol. 2020, Issue 12, Article 132.
FORMULA
MAPLE
seq(numer(sum(1/(2*k-1)^(2*n), k=1..infinity)/Pi^(2*n)), n=1..22);
MATHEMATICA
a[n_]:=Numerator[Pi^(-2 n) (1-2^(-2 n)) Zeta[2 n]] (* Steven Foster Clark, Mar 10 2023 *)
a[n_]:=Numerator[(-1)^n SeriesCoefficient[1/(E^x+1), {x, 0, 2 n-1}]] (* Steven Foster Clark, Mar 10 2023 *)
a[n_]:=Numerator[(-1)^n Residue[Zeta[s] Gamma[s] (1-2^(1-s)), {s, 1-2 n}]] (* Steven Foster Clark, Mar 11 2023 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Martin Renner, Sep 07 2016
STATUS
approved