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%I #12 Mar 02 2024 17:33:47
%S 1,0,6,2,6,9,3,5,4,0,3,8,3,2,1,3,9,3,0,5,6,9,7,5,8,8,4,6,4,8,6,3,4,5,
%T 0,8,0,4,7,4,7,5,1,4,2,6,4,0,0,6,7,2,0,1,2,3,0,1,2,1,1,1,8,1,4,9,6,8,
%U 3,6,4,2,6,3,3,1,5,1,7,6,7,3,0,1,6,7,8,8,5,8,2,0,3,1,8,4,2,8,4,8,1,1,8,3,5,9,9
%N Decimal expansion of - Integral_{x=0..1} log(1 - x)/(x^2 + x) dx.
%H Michael Ian Shamos, <a href="https://citeseerx.ist.psu.edu/doc_view/pid/ae33a269baba5e8b1038e719fb3209e8a00abec5">A catalog of the real numbers</a> (2011), p. 110.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Harmonic_number">Harmonic number</a>.
%F Equals - Integral_{x=0..1} log(1 - x)/(x^2 + x) dx.
%F Equals Pi^2/12 + log(2)^2/2 [Shamos].
%F Equals Sum_{k=>1} H(k)^2/2^(k + 1), where H(k) is the k-th Harmonic number [Shamos].
%F Equals (Pi^2/6 + log(2)^2)/2 = A348373/2
%e 1.062693540383213930569758846486345080474751426...
%t RealDigits[Pi^2/12 + Log[2]^2/2, 10, 120][[1]] (* _Amiram Eldar_, Feb 04 2024 *)
%o (PARI) - intnum(x=0,1,log(1-x)/(x^2+x))
%Y Cf. A000796, A002162, A001008, A002805, A348373.
%K nonn,cons
%O 1,3
%A _Claude H. R. Dequatre_, Feb 04 2024
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