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%I #17 Oct 14 2018 11:37:49
%S 3,1,8,7,7,6,6,2,5,9,2,5,0,2,9,6,7,5,4,8,0,0,8,1,7,6,9,7,7,8,0,1,3,1,
%T 8,1,9,7,2,1,2,4,1,8,6,7,8,7,8,7,0,1,7,0,1,9,7,5,4,9,6,8,1,7,8,9,5,7,
%U 3,2,3,4,2,6,0,2,2,9,9,0,0,6,4,0,9,1
%N Decimal expansion of eta/xi = A086318/A086317, a coefficient associated with the asymptotics of the number of weakly binary trees.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 297.
%H Vincenzo Librandi, <a href="/A245651/b245651.txt">Table of n, a(n) for n = 0..1000</a>
%H Nils Berglund, Christian Kuehn, <a href="https://hal.archives-ouvertes.fr/hal-01432157">Model Spaces of Regularity Structures for Space-Fractional SPDEs</a>, Journal of Statistical Physics, Springer Verlag, 2017, 168 (2), pp.331-368; HAL Id : hal-01432157.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/WeaklyBinaryTree.html">Weakly binary tree</a>
%e 0.31877662592502967548008176977801318197212418678787017019754968178957323426...
%t digits = 103; Clear[c, k]; c[0] = 2; c[n_] := c[n] = c[n-1]^2 + 2; k[n_] := k[n] = (Sqrt[c[n]^2^(-n)]*Sqrt[3 + Sum[1/Product[c[j], {j, 1, k}], {k, 1, n}]])/(c[n]^2^(-n)*(2*Sqrt[Pi])); k[5]; k[n = 10]; While[RealDigits[k[n], 10, digits] != RealDigits[k[n-5], 10, digits], n = n+5]; RealDigits[k[n], 10, digits] // First
%Y Cf. A086317, A086318.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Jul 28 2014
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