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%I #8 Oct 16 2021 06:13:40
%S 2,1,2,5,3,8,7,0,8,0,7,6,6,4,2,7,8,6,1,1,3,9,5,1,7,6,9,2,9,7,2,6,9,0,
%T 1,6,0,9,4,9,5,0,2,8,5,2,8,0,1,3,4,4,0,2,4,6,0,2,4,2,2,3,6,2,9,9,3,6,
%U 7,2,8,5,2,6,6,3,0,3,5,3,4,6,0,3,3,5,7,7,1,6,4,0,6,3,6,8,5,6,9,6,2,3,6,7,1
%N Decimal expansion of Sum_{k>=1} H(k)^2/2^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
%H István Mező, <a href="https://doi.org/10.1016/j.jnt.2012.08.025">A q-Raabe formula and an integral of the fourth Jacobi theta function</a>, Journal of Number Theory, Vol. 133, No. 2 (2013), pp. 692-704.
%H Seán Mark Stewart, <a href="https://doi.org/10.2478/tmmp-2020-0034">Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers</a>, Tatra Mountains Mathematical Publications, Vol. 77, No. 1 (2020), pp. 73-98.
%F Equals Pi^2/6 + log(2)^2 = A013661 + A253191.
%e 2.12538708076642786113951769297269016094950285280134...
%t RealDigits[Pi^2/6 + Log[2]^2, 10, 100][[1]]
%Y Cf. A001008, A002805, A013661, A103930, A103931, A253191.
%Y Similar constants: A016627, A076788.
%K nonn,cons,easy
%O 1,1
%A _Amiram Eldar_, Oct 15 2021
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