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%I #8 Mar 07 2023 10:22:30
%S 1,1,3,6,5,5,9,9,1,8,7,8,6,6,0,0,6,4,3,2,3,6,0,3,4,3,6,6,1,4,0,9,5,3,
%T 4,4,7,3,4,3,8,2,2,8,7,5,0,3,4,3,8,3,3,2,6,1,6,7,2,6,3,8,1,5,6,8,4,3,
%U 1,1,4,7,2,4,7,9,4,4,7,9,4,8,7,4,8
%N Decimal expansion of a coefficient associated with the asymptotics of the average distance between a vertex and the root of a random rooted tree.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 304.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Tree.html">Tree</a>.
%F Average distance for n vertices ~ (1/2)*(2*Pi/beta)^(1/3)*n^(1/2).
%e 1.1365599187866006432360343661409534473438228750343833261672638156843...
%t beta = 0.53494960614230701455037971105206839814311651405699009397707681023752321788064067239783; (* after A086308 and _Vaclav Kotesovec_'s computation *) RealDigits[(1/2)*(2*Pi/beta)^(1/3), 10, 85] // First
%Y Cf. A086308, A245653.
%K nonn,cons,more
%O 1,3
%A _Jean-François Alcover_, Jul 28 2014
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