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Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n and height k (1<=k<=n).
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%I #11 Oct 17 2019 12:20:12

%S 1,1,1,1,3,1,1,6,5,1,1,11,14,7,1,1,19,35,24,9,1,1,32,80,72,36,11,1,1,

%T 53,173,196,123,50,13,1

%N Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n and height k (1<=k<=n).

%H Rigoberto Flórez, Leandro Junes, José L. Ramírez, <a href="https://doi.org/10.1016/j.disc.2019.06.018">Enumerating several aspects of non-decreasing Dyck paths</a>, Discrete Mathematics, Vol. 342, Issue 11 (2019), 3079-3097. See page 3089.

%e Triangle begins:

%e 1,

%e 1,1,

%e 1,3,1,

%e 1,6,5,1,

%e 1,11,14,7,1,

%e 1,19,35,24,9,1,

%e 1,32,80,72,36,11,1,

%e 1,53,173,196,123,50,13,1,

%e ...

%Y Cf. A121460.

%K nonn,tabl,more

%O 1,5

%A _N. J. A. Sloane_, Oct 16 2019