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%I #5 Jun 07 2016 11:04:40
%S 9,9,9,2,2,2,8,3,7,7,6,3,8,3,0,0,0,8,7,6,1,9,3,5,7,4,9,2,4,7,5,6,9,8,
%T 8,6,0,3,6,9,9,5,5,1,6,1,3,6,1,7,0,9,4,4,2,0,4,8,9,8,4,3,5,8,6,2,7,6,
%U 1,0,2,2,9,7,3,5,5,0,1,2,4,2,2,2,1,9,6,3,5,3,5,0,3,5,5,9,7,6,4,7,3,9,2
%N Decimal expansion of a doubly infinite sum involving harmonic numbers. Curiously, this sum is very close to 1.
%H R. Pemantle, C. Schneider, <a href="http://arxiv.org/abs/math/0511574">When is 0.999... equal to 1?</a>, arXiv:math/0511574 [math.CO], 2005.
%F Sum_{j >= 1, k >= 1} H(j) (H(k+1)-1)/(j k (k+1) (j+k)), where H(j) is the j-th harmonic number.
%F Equals -4 zeta(2) - 2 zeta(3) + 4 zeta(2) zeta(3) + 2 zeta(5).
%e 0.99922283776383000876193574924756988603699551613617094420489843586276...
%t RealDigits[-4 Zeta[2] - 2 Zeta[3] + 4 Zeta[2] Zeta[3] + 2 Zeta[5], 10,
%t 103][[1]]
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Jun 07 2016
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