%I #22 Dec 04 2018 16:57:53
%S 1,1,1,2,2,1,4,5,3,1,9,12,9,4,1,21,30,25,14,5,1,49,74,69,44,20,6,1,
%T 115,182,185,133,70,27,7,1,269,444,488,386,230,104,35,8,1,630,1078,
%U 1266,1090,718,369,147,44,9,1,1474,2605,3245,3006,2161,1232,560,200,54,10,1
%N Triangle read by rows: T(n,k) is the number of nondecreasing Motzkin prefixes (i.e., left factors of nondecreasing Motzkin 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 - x - 2*x^2 + x^3)/(1 - 2*x - 2*x^2 + 3x^3 - x^5),(x*(1-x)^2*(1+x))/(1 - 2*x - x^2 + 2*x^3 - x^4)).
%e Triangle begins:
%e 1;
%e 1, 1;
%e 2, 2, 1;
%e 4, 5, 3, 1;
%e 9, 12, 9, 4, 1;
%e 21, 30, 25, 14, 5, 1;
%e 49, 74, 69, 44, 20, 6, 1;
%e 115, 182, 185, 133, 70, 27, 7, 1;
%e 269, 444, 488, 386, 230, 104, 35, 8, 1;
%e 630, 1078, 1266, 1090, 718, 369, 147, 44, 9, 1;
%e 1474, 2605, 3245, 3006, 2161, 1232, 560, 200, 54, 10, 1;
%e ...
%Y Column k=0 gives A322325.
%Y Cf. A097862, A283595.
%K nonn,tabl
%O 0,4
%A _José Luis Ramírez Ramírez_, Dec 03 2018