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A306774 Decimal expansion of Sum_{k>=2} (-1)^k * zeta(k) * zeta(2*k) / k.

%I A306774 #8 Feb 16 2025 08:33:55
%S A306774 6,3,8,9,0,6,1,6,2,6,1,6,2,7,4,0,9,1,2,0,6,3,9,8,2,7,8,1,4,1,1,1,7,4,
%T A306774 9,8,8,2,8,4,3,8,9,1,3,1,3,5,1,1,5,9,8,3,5,1,8,5,5,4,5,4,5,0,5,4,8,3,
%U A306774 1,7,6,2,0,9,0,6,3,0,8,4,6,3,0,7,3,5,2,9,1,8,3,9,6,4,4,7,5,5,2,4,3,6,2,5,6,4
%N A306774 Decimal expansion of Sum_{k>=2} (-1)^k * zeta(k) * zeta(2*k) / k.
%H A306774 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>
%H A306774 Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>
%F A306774 Equals log(A303670) + A001620 * Pi^2/6.
%e A306774 0.63890616261627409120639827814111749882843891313511598351855454505483176209...
%p A306774 evalf(Sum((-1)^k*Zeta(k)*Zeta(2*k)/k, k=2..infinity), 100);
%o A306774 (PARI) sumalt(k=2, (-1)^k*zeta(k)*zeta(2*k)/k)
%Y A306774 Cf. A303670, A306769, A306778.
%K A306774 nonn,cons
%O A306774 0,1
%A A306774 _Vaclav Kotesovec_, Mar 09 2019