A073147 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).

1, 1, 2, 3, 4, 7, 12, 15, 18, 30, 55, 67, 76, 88, 143, 273, 328, 364, 400, 455, 728, 1428, 1701, 1866, 2010, 2175, 2448, 3876, 7752, 9180, 9999, 10659, 11319, 12138, 13566, 21318, 43263

Offset: 0

Author

Paul D. Hanna, Jul 18 2002

Keywords

• easy
• nonn
• tabl

Comments

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).

These numbers are cardinalities of some intervals in the Tamari lattices. - F. Chapoton, Jul 15 2021

Examples

			{1}, {1,2}, {3,4,7}, {12,15,18,30}, {55,67,76,88,143}, {273,328,364,400,455,728},...
		

Crossrefs

Cf. A001764, A006013, A006629, A028364.

Formula

(n, m)-th entry in triangle is Sum A001764(n-k)*A001764(k), k=0..m.