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A245653 Decimal expansion of a coefficient associated with the asymptotics of the variance of the distance between a vertex and the root of a random rooted tree.

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%I A245653 #8 Feb 16 2025 08:33:23
%S A245653 3,5,2,9,6,2,2,2,2,9,0,5,8,7,7,1,1,1,6,0,8,0,3,4,8,7,4,4,0,4,9,9,6,1,
%T A245653 2,9,2,9,2,7,5,2,5,3,9,5,3,0,6,2,3,2,2,3,3,8,9,5,6,7,2,5,5,8,1,9,7,6,
%U A245653 2,7,4,0,5,8,3,3,4,8,6,4,6,1,0,4,1
%N A245653 Decimal expansion of a coefficient associated with the asymptotics of the variance of the distance between a vertex and the root of a random rooted tree.
%D A245653 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 304.
%H A245653 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Tree.html">Tree</a>.
%F A245653 Variance of distance for n vertices ~ ((4-Pi)/(4*Pi))*(2*Pi/beta)^(2/3)*n.
%e A245653 0.35296222290587711160803487440499612929275253953062322338956725581976274...
%t A245653 beta = 0.53494960614230701455037971105206839814311651405699009397707681023752321788064067239783; (* after A086308 and _Vaclav Kotesovec_'s computation *) RealDigits[((4-Pi)/(4*Pi))*(2*Pi/beta)^(2/3), 10, 85] // First
%Y A245653 Cf. A086308, A245652.
%K A245653 nonn,cons,more
%O A245653 0,1
%A A245653 _Jean-François Alcover_, Jul 28 2014