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%I #16 Feb 25 2020 11:26:19
%S 1,0,1,1,0,1,0,2,0,1,2,0,3,0,1,0,5,0,4,0,1,5,0,9,0,5,0,1,0,13,0,14,0,
%T 6,0,1,13,0,26,0,20,0,7,0,1,0,34,0,45,0,27,0,8,0,1,34,0,73,0,71,0,35,
%U 0,9,0,1,0,89,0,137,0,105,0,44,0,10,0,1,89,0,201,0,234,0,148,0,54,0,11,0,1,0,233,0,402,0,373,0,201,0,65,0,12,0,1,233,0,546,0,733,0,564,0,265,0,77,0,13,0,1,0,610,0,1149,0,1245,0,818,0,341,0,90,0,14,0,1
%N Triangle read by rows: T(n,k) is the number of nondecreasing Dyck prefixes (i.e., left factors of nondecreasing Dyck paths) of length n and final height k (0 <= k <= n).
%H R. Flórez and J. L. Ramírez, <a href="https://ajc.maths.uq.edu.au/pdf/72/ajc_v72_p138.pdf">Some enumerations on non-decreasing Motzkin paths</a>, Australasian Journal of Combinatorics, 72(1) (2018), 138-154.
%F Riordan array: ((1 - 2*x^2)/(1 - 3*x^2 + x^4), (x*(1-x^2))/(1 - 2*x^2)).
%e Triangle begins:
%e 1;
%e 0, 1;
%e 1, 0, 1;
%e 0, 2, 0, 1;
%e 2, 0, 3, 0, 1;
%e 0, 5, 0, 4, 0, 1;
%e 5, 0, 9, 0, 5, 0, 1;
%e 0, 13, 0, 14, 0, 6, 0, 1;
%e 13, 0, 26, 0, 20, 0, 7, 0, 1;
%e 0, 34, 0, 45, 0, 27, 0, 8, 0, 1;
%e 34, 0, 73, 0, 71, 0, 35, 0, 9, 0, 1;
%e 0, 89, 0, 137, 0, 105, 0, 44, 0, 10, 0, 1;
%e 89, 0, 201, 0, 234, 0, 148, 0, 54, 0, 11, 0, 1;
%e 0, 233, 0, 402, 0, 373, 0, 201, 0, 65, 0, 12, 0, 1;
%e ...
%Y Columns k=0, 1 give A001519. Column k=2 gives A061667.
%Y Cf. A322329, A322325.
%K nonn,tabl
%O 0,8
%A _José Luis Ramírez Ramírez_, Dec 05 2018
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