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%I #21 Jan 03 2025 02:00:51
%S 2,7,0,9,7,5,6,4,2,4,9,6,7,4,0,0,7,0,1,8,3,0,1,3,6,1,4,1,0,7,4,1,1,1,
%T 2,2,6,8,0,7,2,8,3,9,9,0,1,2,5,9,4,6,8,7,4,5,1,1,4,8,8,1,7,1,9,3,5,7,
%U 6,2,7,8,9,9,8,4,4,8,8,3,8,1,3,6,6,2,2,5,8,9,7,9,2,9,7,8,8,9,6,6,2,6,2,9,2
%N Decimal expansion of Ni_2 = gamma/3 - log(2*Pi)/2 - 2*zeta'(-1) + 2/3, where gamma = A001620.
%H Marc-Antoine Coppo, <a href="https://doi.org/10.1016/j.jmaa.2019.03.057">A note on some alternating series involving zeta and multiple zeta values</a>, Journal of Mathematical Analysis and Applications Volume 475, Issue 2, 15 July 2019, Pages 1831-1841.
%F Equals Sum_{s>=2} (-1)^(s)*zeta(s)/(s+2).
%F Equals A001620/3 - log(2*A000796)/2 + 2*log(A074962) + 1/2.
%e 0.270975642496740070183013614107411122680728399012594687451148817...
%t RealDigits[EulerGamma/3 - Log[2 Pi]/2 + 2/3 - 2 Zeta'[-1], 10, 105][[1]]
%Y Cf. A000796, A001620, A074962, A131688 (Ni_-1), A321943 (Ni_1), A379751 (Ni_3).
%K cons,nonn
%O 0,1
%A _Artur Jasinski_, Dec 22 2024