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%I #9 Jun 04 2014 10:09:00
%S 6,8,2,1,5,5,5,6,7,1,0,0,6,2,7,3,1,6,1,6,7,1,5,5,2,6,2,3,7,9,0,5,0,8,
%T 3,3,0,0,3,8,6,8,1,0,0,0,1,6,8,8,8,5,9,9,1,0,9,0,6,5,5,1,0,1,3,4,2,2,
%U 0,8,6,2,6,5,8,2,1,7,7,1,5,9,8,1,1,4,8,8,6,8,9,0,5,4,5,3,9,9,8,1
%N Decimal expansion of the positive solution to the equation x/(1-x) = 1+log(1/(1-x)), an auxiliary constant associated with the problem of enumeration of trees by inversions.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6, p. 303.
%H I. M. Gessel, B. E. Sagan, Y. N. Yeh, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.865">Enumeration of Trees By Inversions</a>, 1999, p. 20.
%e 0.6821555671006273161671552623790508330038681...
%t mu = x /. FindRoot[x/(1-x) == 1+Log[1/(1-x)], {x, 1/2}, WorkingPrecision -> 105]; RealDigits[mu, 10, 100] // First
%Y Cf. A038037.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, May 22 2014
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