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%I #19 Jan 12 2020 11:27:33
%S 1,1,1,1,1,0,1,1,1,0,1,1,2,1,0,1,1,2,4,1,0,1,1,2,5,6,1,0,1,1,2,5,13,8,
%T 1,0,1,1,2,5,14,28,10,1,0,1,1,2,5,14,41,48,12,1,0
%N Array read by antidiagonals upwards: T(n,k) (n>=1, k>=0) = number of Dyck paths of semilength k avoiding the pattern U^(n-1) D^(n-1) U D.
%H Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani, and Julian West, <a href="http://dx.doi.org/10.1016/j.disc.2013.12.011">The Dyck pattern poset</a> Discrete Math. 321 (2014), 12--23. MR3154009.
%e Array begins (the columns correspond to k = 0, 1, 2, ..., the rows to n = 1, 2, 3, ...):
%e 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 1, 2, 4, 6, 8, 10, 12, 14, 16, ...
%e 1, 1, 2, 5, 13, 28, 48, 73, 103, 138, ...
%e 1, 1, 2, 5, 14, 41, 110, 245, 450, 739, ...
%e 1, 1, 2, 5, 14, 42, 131, 397, 1069, 2427, ...
%e 1, 1, 2, 5, 14, 42, ...
%e ...
%Y Cf. A000108 (limit of rows). Row k=4 is A225690, k=5 is A225691.
%K nonn,tabl,more
%O 1,13
%A _N. J. A. Sloane_, Feb 21 2014
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