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%I #15 Sep 08 2022 08:46:11
%S 4,6,4,8,4,7,6,9,9,1,7,0,8,0,5,1,0,7,4,9,2,6,9,2,4,8,6,8,3,2,9,3,9,0,
%T 6,0,8,8,2,9,4,1,1,8,7,5,7,5,9,0,1,0,8,3,7,9,1,1,7,1,5,7,1,4,8,5,0,9,
%U 6,0,4,2,3,7,2,8,6,2,5,4,0,6,2,8,0,9,2,6,5,6,0,5,2,2,3,8,7,3,0,7,9,4,4,7,3
%N Decimal expansion of Sum_{k>=0} zeta(2k)/((2k+1)*4^(2k)) (negated).
%H G. C. Greubel, <a href="/A256318/b256318.txt">Table of n, a(n) for n = 0..10000</a>
%H H. M. Srivasata, M. L. Glasser, and Victor S. Adamchik, <a href="https://kilthub.cmu.edu/articles/journal%20contribution/Some_Definite_Integrals_Associated_with_the_Riemann_Zeta_Function/6609653/1">Some Definite Integrals Associated with the Riemann Zeta Function</a>
%F Equals -G/Pi - log(2)/4, where G is Catalan's constant.
%e -0.464847699170805107492692486832939060882941187575901...
%t RealDigits[-Catalan/Pi - Log[2]/4, 10, 105] // First
%o (PARI) Catalan/Pi + log(2)/4 \\ _Charles R Greathouse IV_, Mar 23 2015
%o (PARI) .5 - sumpos(k=1,zeta(2*k)/(2*k+1)/16^k) \\ _Charles R Greathouse IV_, Mar 23 2015
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Catalan(R)/Pi(R) + Log(2)/4; // _G. C. Greubel_, Aug 25 2018
%Y Cf. A006752, A256319.
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Mar 23 2015
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