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A306769 Decimal expansion of Sum_{k>=2} (-1)^k * Zeta(k)^2 / k.

%I A306769 #20 Feb 16 2025 08:33:55
%S A306769 1,0,4,3,4,0,2,9,1,7,5,7,4,2,8,8,7,3,3,2,5,5,2,8,9,6,4,6,6,7,1,6,7,6,
%T A306769 0,3,0,5,4,8,4,7,0,8,6,6,0,4,6,8,8,2,5,6,1,0,4,4,5,7,0,4,7,9,7,6,9,5,
%U A306769 8,5,0,6,2,5,5,2,5,2,4,8,4,3,2,7,6,1,5,1,0,7,2,0,7,9,8,4,1,4,3,5,6,2,1,4,6
%N A306769 Decimal expansion of Sum_{k>=2} (-1)^k * Zeta(k)^2 / k.
%C A306769 Sum_{k>=2} (-1)^k*Zeta(k)/k = A001620 (see MathWorld, formula 122).
%H A306769 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>
%H A306769 Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>
%F A306769 Equals log(A306765) + A001620^2.
%e A306769 1.043402917574288733255289646671676030548470866046882561044570479769585...
%p A306769 evalf(Sum((-1)^j*Zeta(j)^2/j, j=2..infinity), 100);
%t A306769 NSum[(-1)^k*Zeta[k]^2/k, {k, 2, Infinity}, WorkingPrecision -> 200, NSumTerms -> 100000]
%o A306769 (PARI) sumalt(k=2, (-1)^k*zeta(k)^2/k) \\ _Michel Marcus_, Mar 09 2019
%Y A306769 Cf. A231132, A306760, A306765, A306774, A306778, A307106.
%K A306769 nonn,cons
%O A306769 1,3
%A A306769 _Vaclav Kotesovec_, Mar 09 2019