A379751 - OEIS

%I #6 Jan 03 2025 02:01:04

%S 2,1,3,6,1,6,7,7,6,2,8,0,2,1,6,7,8,2,0,0,5,6,3,6,0,0,8,7,6,3,1,9,3,8,

%T 9,9,5,8,3,5,8,3,3,8,4,0,5,1,2,1,4,3,6,2,4,5,8,2,7,4,8,5,1,0,6,6,7,5,

%U 0,2,1,4,2,6,5,4,0,9,9,2,5,6,1,8,0,1,8,3,4,6,8,7,5,2,1,8,6,0,1,7,9,4,0,3,5

%N Decimal expansion of Ni_3 = gamma/4 - log(2*Pi)/2 - 3*zeta'(-1) + 3*zeta'(-2) + 7/12, 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+3).

%t RealDigits[EulerGamma/4 - Log[2 Pi]/2 - 3 Zeta'[-1] + 3 Zeta'[-2] + 7/12, 10, 105][[1]]

%Y Cf. A000796, A001620, A074962, A131688 (Ni_-1), A321943 (Ni_1), A379425 (Ni_2).

%K cons,nonn

%O 0,1

%A _Artur Jasinski_, Jan 01 2025