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%I #5 Sep 17 2014 11:28:10
%S 2,1,1,7,1,4,1,7,3,4,7,7,7,0,3,9,4,1,1,1,2,9,1,0,0,2,2,6,0,1,2,4,5,1,
%T 7,5,1,9,1,7,6,8,0,7,6,6,9,1,6,0,8,4,0,6,9,3,6,7,6,6,3,9,0,2,7,0,4,9,
%U 4,8,2,1,2,9,8,0,6,7,5,0,9,4,9,6,0,3,6,2,6,6,0,6,8,7,7,9,0,4,6,6,3,4,5,5
%N Decimal expansion of c(4), a constant appearing in certain Euler double sums not expressible in terms of well-known constants.
%H J. M. Borwein, I.J. Zucker and J. Boersma, <a href="http://carma.newcastle.edu.au/MZVs/mzv-week05.pdf">The evaluation of character Euler double sums</a>, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 17 c(4).
%F c(n) = sum_{k=0..n-2} (n-2)!/k!*log(2)^k*Li_(n-k)(1/2) + log(2)^n/n.
%F c(4) = (1/12)*((-Pi^2)*log(2)^2 + log(2)^4 + 24*Li_4(1/2) + 21*log(2)*zeta(3)).
%e 2.117141734777039411129100226012451751917680766916084...
%t c[4] = (1/12)*((-Pi^2)*Log[2]^2 + Log[2]^4 + 24*PolyLog[4, 1/2] + 21*Log[2]*Zeta[3]); RealDigits[c[4], 10, 104] // First
%Y Cf. A002162 c(1), A072691 c(2), A233091 c(3).
%K nonn,cons,easy
%O 1,1
%A _Jean-François Alcover_, Sep 17 2014
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