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%I #39 Jan 02 2014 02:09:14
%S 4,5,9,9,8,7,3,7,4,3,2,7,2,3,3,7,3,1,3,9,4,3,0,1,5,7,1,0,2,9,9,9,6,3,
%T 5,8,6,7,9,2,6,9,1,5,4,5,6,5,4,5,8,9,3,5,7,6,5,2,6,4,8,9,1,5,6,3,7,5,
%U 1,2,6,1,8,7,9,4,6,1,7,5,9,7,8,6,6,8,6,5,9,5,2,7,5,2,2,2,4,6,4,8
%N Decimal expansion of sum_{k=1..infinity} (H(k)/k)^2, where H(k) = sum_{j=1..k} 1/j.
%C Also, decimal expansion of 17/(22*Pi)*integral_{t=0..Pi} ((Pi-t)^2*log(2*sin(t/2))^2 dt.
%H D. H. Bailey and J. M. Borwein, <a href="http://escholarship.org/uc/item/6b6986dn#page-9">Euler's Multi-Zeta Sums</a>
%F Equals 17*zeta(4)/4 = 17*Pi^4/360 = (17/4) * sum_{k=1..infinity} 1/k^4.
%e 4.5998737432723373139430157102999635867926915456545893...
%t 17*Pi^4/360 // N[#, 100] & // RealDigits // First
%K nonn,cons
%O 1,1
%A _Jean-François Alcover_, Mar 28 2013
%E Offset corrected by _Rick L. Shepherd_, Jan 01 2014
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