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A256921 Decimal expansion of Sum_{k>=2} zeta(k)/(k*2^k).

%I A256921 #30 Feb 16 2025 08:33:25
%S A256921 2,8,3,7,5,7,1,1,0,4,7,3,9,3,3,6,5,6,7,6,8,4,5,7,6,3,0,6,3,5,3,2,8,1,
%T A256921 4,0,3,0,2,5,6,7,7,3,8,4,8,7,6,9,3,9,8,6,3,5,3,9,2,7,9,1,8,2,9,3,6,3,
%U A256921 5,0,2,1,5,5,3,5,8,0,7,0,4,4,2,3,3,3,8,1,0,3,4,9,1,8,7,1,4,7,9,0,9,3,6,8,9
%N A256921 Decimal expansion of Sum_{k>=2} zeta(k)/(k*2^k).
%D A256921 H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 272.
%H A256921 G. C. Greubel, <a href="/A256921/b256921.txt">Table of n, a(n) for n = 0..10000</a>
%H A256921 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>
%H A256921 Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>
%F A256921 Equals (1/2)*log(Pi) - EulerGamma/2.
%F A256921 Equals Sum_{k>0} (-1)^(k+1)*(H(k)-log(k)-EulerGamma), where H(k) is the k-th harmonic number.
%F A256921 Equals -Sum_{k>=1} (1/(2*k) + log(1 - 1/(2*k))). - _Amiram Eldar_, Jul 22 2020
%e A256921 0.2837571104739336567684576306353281403025677384876939863539279...
%t A256921 RealDigits[(1/2)*Log[Pi] - EulerGamma/2, 10, 105] // First
%o A256921 (PARI) log(Pi)/2 - Euler/2 \\ _Michel Marcus_, Apr 13 2015
%o A256921 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (Log(Pi(R)) - EulerGamma(R))/2; // _G. C. Greubel_, Sep 04 2018
%Y A256921 Cf. A001620, A053510, A256922.
%K A256921 nonn,cons,easy
%O A256921 0,1
%A A256921 _Jean-François Alcover_, Apr 13 2015