A073148 Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(n,0)=A006013(n), a(n+1,n)=A001764(n+1), a(n,m) = Sum A001764(n-k)*a(n,k), k=0..m.

1, 2, 3, 7, 9, 12, 30, 37, 43, 55, 143, 173, 194, 218, 273, 728, 871, 961, 1045, 1155, 1428, 3876, 4604, 5033, 5393, 5778, 6324, 7752, 21318, 25194, 27378, 29094, 30744, 32655, 35511, 43263, 120175

Offset

0,2

Comments

Compare to A073147. Related to generalized Catalan numbers; in particular, C(3n,n)/(2n+1) (enumerates ternary trees and also non-crossing trees)(A001764).

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

Links

Table of n, a(n) for n=0..36.

Formula

a(n, m) = Sum A001764(n-k)*a(n, k), k=0..m.

Example

{1}, {2,3}, {7,9,12}, {30,37,43,55}, {143,173,194,218,273},{728,871,961,1045,1155,1428}, {3876,4604,5033,5393,5778,6324,7752}, ...

Crossrefs

Cf. A073147, A001764, A006013, A006629, A028364.

Sequence in context: A077510 A364052 A178433 * A014839 A262775 A092293

Adjacent sequences: A073145 A073146 A073147 * A073149 A073150 A073151

Keyword

easy,nonn,tabl

Author

Paul D. Hanna, Jul 18 2002

Status

approved