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%I #15 Sep 08 2023 01:22:37
%S 1,1,2,5,14,41,124,385,1221,3939,12886,42648,142544,480459,1631287,
%T 5574073,19153815,66146259,229452587,799140681,2793373937,9796395680,
%U 34459558856,121548541383,429823475811,1523511450184,5411789548439
%N Number of n-leaf binary trees that do not contain (()(()(()((()())())))) as a subtree.
%C By 'binary tree' we mean a rooted, ordered tree in which each vertex has either 0 or 2 children.
%H CombOS - Combinatorial Object Server, <a href="http://combos.org/btree">Generate binary trees</a>
%H Petr Gregor, Torsten Mütze, and Namrata, <a href="https://arxiv.org/abs/2306.08420">Combinatorial generation via permutation languages. VI. Binary trees</a>, arXiv:2306.08420 [cs.DM], 2023.
%H Eric S. Rowland, <a href="http://arxiv.org/abs/0809.0488">Pattern avoidance in binary trees</a>, arXiv:0809.0488 [math.CO], 2008-2010.
%F G.f. f(x) satisfies -x f(x)^3 + (x-1) x f(x)^2 + (x-1)^2 f(x) + (x-1) x = 0.
%K nonn
%O 1,3
%A _Eric Rowland_, Apr 23 2009