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A295568 Irregular triangle, read by rows: the Catalan generating tree, read from left to right, row by row, starting at the root.

%I A295568 #26 Dec 02 2017 10:12:52
%S A295568 2,2,3,2,3,2,3,4,2,3,2,3,4,2,3,2,3,4,2,3,4,5,2,3,2,3,4,2,3,2,3,4,2,3,
%T A295568 4,5,2,3,2,3,4,2,3,2,3,4,2,3,4,5,2,3,2,3,4,2,3,4,5,2,3,4,5,6,2,3,2,3,
%U A295568 4,2,3,2,3,4,2,3,4,5,2,3,2,3,4,2,3,2,3,4,2,3,4,5,2,3,2,3,4,2,3,4,5,2,3,4,5,6
%N A295568 Irregular triangle, read by rows: the Catalan generating tree, read from left to right, row by row, starting at the root.
%C A295568 Row n has Catalan(n) terms.
%C A295568 The rows converge to A076050.
%H A295568 Rémy Sigrist, <a href="/A295568/b295568.txt">Rows n = 1..10 of triangle, flattened</a>
%H A295568 D. Kremer, <a href="https://doi.org/10.1016/S0012-365X(99)00302-7">Permutations with forbidden subsequences and a generalized Schröder number</a>, Discrete Math. 218 (2000) 121-130.
%H A295568 Julian West, <a href="http://dx.doi.org/10.1016/0012-365X(94)00067-1">Generating trees and the Catalan and Schröder numbers</a>, Discrete Math. 146 (1995), 247-262.
%H A295568 Julian West, <a href="https://doi.org/10.1016/S0012-365X(96)83023-8">Generating trees and forbidden subsequences</a>, Discrete Math., 157 (1996), 363-374.
%e A295568 The triangle starts with a root node (at level 1) labeled 2; thereafter every node labeled k has k children at the next level whose labels are 2, 3, 4, ..., k, k+1.
%e A295568 Rows 1, 2, 3, 4, 5, and part of 6 are:
%e A295568 2,
%e A295568 2, 3,
%e A295568 2, 3, 2, 3, 4,
%e A295568 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5,
%e A295568 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6,
%e A295568 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6, ...
%e A295568 ...
%Y A295568 Cf. A000108, A076050, A295569.
%K A295568 nonn,tabf
%O A295568 1,1
%A A295568 _N. J. A. Sloane_, Nov 29 2017