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%I #9 Jul 15 2021 15:07:21
%S 1,1,2,3,4,7,12,15,18,30,55,67,76,88,143,273,328,364,400,455,728,1428,
%T 1701,1866,2010,2175,2448,3876,7752,9180,9999,10659,11319,12138,13566,
%U 21318,43263
%N Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(n,0)=A001764(n), a(n,n)=A006013(n), a(n,n-1)=A006629(n-1).
%C Related to generalized Catalan numbers; in particular, C(3n,n)/(2n+1) (enumerates ternary trees and also non-crossing trees)(A001764) and sum of root degrees of all noncrossing trees on nodes on a circle (A006629).
%C These numbers are cardinalities of some intervals in the Tamari lattices. - _F. Chapoton_, Jul 15 2021
%F (n, m)-th entry in triangle is Sum A001764(n-k)*A001764(k), k=0..m.
%e {1}, {1,2}, {3,4,7}, {12,15,18,30}, {55,67,76,88,143}, {273,328,364,400,455,728},...
%Y Cf. A001764, A006013, A006629, A028364.
%K easy,nonn,tabl
%O 0,3
%A _Paul D. Hanna_, Jul 18 2002