A334450 - OEIS
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COMMENTS
In general, for s>0, Product_{k>=1} (1 + 1/A002144(k)^(2*s+1))/(1 - 1/A002144(k)^(2*s+1)) = Pi^(2*s+1) * A000364(s) * zeta(2*s+1) / ((2^(2*s+2) + 2) * (2*s)! * zeta(4*s+2)). - Dimitris Valianatos, May 01 2020
In general, for s>1, Product_{k>=1} (1 + 1/A002144(k)^s)/(1 - 1/A002144(k)^s) = (zeta(s, 1/4) - zeta(s, 3/4)) * zeta(s) / (2^s * (2^s + 1) * zeta(2*s)).
REFERENCES
B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, p. 64-65.
EXAMPLE
0.999676527079626662018246180873083701500751574379554430568432840424975981921219...