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A318945 Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = number of Dyck paths with k valleys of altitude k.

%I A318945 #10 Sep 19 2018 05:44:34
%S A318945 1,4,1,13,5,1,39,19,6,1,112,64,26,7,1,313,201,97,34,8,1,859,603,331,
%T A318945 139,43,9,1,2328,1752,1064,512,191,53,10,1
%N A318945 Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = number of Dyck paths with k valleys of altitude k.
%H A318945 Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L., <a href="https://doi.org/10.1016/j.disc.2018.06.032">Enumerations of peaks and valleys on non-decreasing Dyck paths</a>, Discrete Mathematics (2018), 341(10), 2789-2807.
%e A318945 Triangle begins:
%e A318945 1,
%e A318945 4,1,
%e A318945 13,5,1,
%e A318945 39,19,6,1,
%e A318945 112,64,26,7,1,
%e A318945 313,201,97,34,8,1,
%e A318945 859,603,331,139,43,9,1,
%e A318945 2328,1752,1064,512,191,53,10,1,
%e A318945 ...
%Y A318945 Columns 0, 1, 2. 3 are A105693, A318946, A318947, A319405.
%K A318945 nonn,tabl,more
%O A318945 2,2
%A A318945 _N. J. A. Sloane_, Sep 18 2018