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%I A243395 #6 Jun 04 2014 13:43:26
%S A243395 1,1,5,7,4,1,9,8,0,3,8,1,9,2,8,0,2,6,4,4,8,2,6,3,5,4,5,0,8,4,0,9,4,6,
%T A243395 2,5,4,6,8,6,4,2,8,6,2,7,9,7,0,4,1,9,4,1,3,4,2,2,0,5,2,6,8,2,4,5,2,0,
%U A243395 2,3,9,8,7,8,5,9,4,4,2,3,7,7,0,0,3,0,4,5,7,5,5,8,4,5,0,6,6,8,4,2,3,8,2,6
%N A243395 Decimal expansion of 'xiHat', a constant used in the asymptotic evaluation of e.g.f. coefficients for the number of labeled mobiles.
%D A243395 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's tree enumeration constants, p. 303.
%F A243395 A038037 = Numerator of n-th coefficient ~ etaHat * xiHat^n * n^(n-1), where etaHat is A243396.
%e A243395 1.15741980381928026448263545084...
%t A243395 digits = 104; mu = x /. FindRoot[x/(1 - x) == 1 + Log[1/(1 - x)], {x, 1/2}, WorkingPrecision -> digits + 5] ; xiHat = E^-1*(1 - mu)^-1; RealDigits[xiHat, 10, digits] // First
%Y A243395 Cf. A038037, A242769, A243396.
%K A243395 nonn,cons
%O A243395 1,3
%A A243395 _Jean-François Alcover_, Jun 04 2014