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%I #30 Sep 12 2022 11:43:39
%S 1,1,5,9,3,1,5,1,5,6,5,8,4,1,2,4,4,8,8,1,0,7,2,0,0,3,1,3,7,5,7,7,4,1,
%T 3,7,0,3,3,3,4,0,7,9,8,4,2,0,3,3,1,6,5,5,3,1,4,9,1,2,7,7,4,6,0,8,5,2,
%U 5,8,9,5,1,9,2,0,3,0,0,4,4,6,6,8,9,1,6,2,6,3,7,0,4,6,7,1,9,3,8,0,2,7,3,7
%N Decimal expansion of Sum_{k>=1} zeta(2*k+1)/((2*k+1)*2^(2*k)).
%H G. C. Greubel, <a href="/A255681/b255681.txt">Table of n, a(n) for n = 0..10000</a>
%H H. M. Srivastava and Junesang Choi, <a href="https://doi.org/10.1016/C2010-0-67023-4">Zeta and q-Zeta Functions and Associated Series and Integrals</a>, Elsevier Insights, 2011, pp. 272 and 314.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>.
%F Equals log(2) - EulerGamma.
%F Equals Sum_{k>=1} (zeta(2*k+1)-1)/(k+1). - _Amiram Eldar_, May 24 2021
%F Equals Sum_{k>=1} psi(k)/2^k, where psi(x) is the digamma function. - _Amiram Eldar_, Sep 12 2022
%e 0.1159315156584124488107200313757741370333407984203316553149...
%t RealDigits[Log[2] - EulerGamma, 10, 105] // First
%o (PARI) default(realprecision, 100); log(2) - Euler \\ _G. C. Greubel_, Sep 06 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Log(2) - EulerGamma(R); // _G. C. Greubel_, Sep 06 2018
%Y Cf. A001620, A002162, A094642 (= log(Pi/2) = Sum_{k>=2} zeta(2*k)/(k*2^(2*k))).
%K nonn,cons,easy
%O 0,3
%A _Jean-François Alcover_, Apr 13 2015
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