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%I #6 Jan 05 2025 19:51:42
%S 1,2,7,6,3,0,5,1,5,9,4,3,5,1,3,8,8,3,5,1,8,4,9,1,7,1,0,3,2,1,5,1,8,3,
%T 3,7,4,2,4,1,8,1,2,9,3,6,5,9,7,4,2,5,4,0,4,1,2,7,4,7,6,9,3,9,0,5,1,9,
%U 0,0,4,3,9,4,6,0,3,6,2,9,5,5,2,5,6,3,1,1,5,3,6,5,8,4,5,5,9,1,8,0,4,9,9,0,5
%N Decimal expansion of Pi^2*log(2)/6 - log(2)^3/3 - 3*zeta(3)/4.
%H Ovidiu Furdui, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Problems/Adv2014Nov.pdf">Problem H-761</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 52, No. 4 (2014), p. 374; <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Problems/August2016AdvProbSln.pdf">A Series Whose Sum Involves Pi, ln 2 and zeta(3)</a>, Solution to Problem H-761 by AN-anduud Problem Solving Group, ibid., Vol. 54, No. 3 (2016), pp. 283-285.
%F Equals Sum_{n>=1} ((1/n) * (Sum_{k>=1} (-1)^(k+1)/(n+k))^2).
%e 0.12763051594351388351849171032151833742418129365974...
%t RealDigits[Pi^2*Log[2]/6 - Log[2]^3/3 - 3*Zeta[3]/4, 10, 100][[1]]
%Y Cf. A000796, A002117, A002162, A013661, A197070.
%K nonn,cons
%O 0,2
%A _Amiram Eldar_, Jan 14 2022