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%I #14 Apr 19 2016 02:21:34
%S 7,9,1,6,0,3,1,8,3,5,7,7,5,1,1,8,0,7,8,2,3,6,2,8,4,5,5,7,2,3,2,6,8,2,
%T 2,4,0,7,1,7,4,2,4,1,8,0,9,0,7,8,9,4,6,7,3,1,2,3,0,7,8,3,0,9,9,2,2,9,
%U 0,4,4,1,5,0,3,8,9,3,2,9,2,5,5,4,4,6,6,7,9,0,8,6,8,4,0,4,6,3,0,3,8,3
%N Decimal expansion of asymptotic constant eta for counts of weakly binary trees.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WeaklyBinaryTree.html">Weakly binary tree</a>
%F Equals lim n -> infinity A001190(n)*n^(3/2)/A086317^(n-1). - _Vaclav Kotesovec_, Apr 19 2016
%e 0.791603183577511807823628455723268224071742418090789...
%t digits = 102; c[0] = 2; c[n_] := c[n] = c[n - 1]^2 + 2; eta[n_Integer] := eta[n] = 1/2 * Sqrt[c[n]^2^(-n)/Pi] * Sqrt[3 + Sum[1/Product[c[j], {j, 1, k}], {k, 1, n}]]; eta[5]; eta[n = 10]; While[RealDigits[eta[n], 10, digits] != RealDigits[eta[n - 5], 10, digits], n = n + 5]; RealDigits[eta[n], 10, digits] // First (* _Jean-François Alcover_, May 27 2014 *)
%Y Cf. A001190, A086317.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Jul 15 2003
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