A115965 Number of planar subpartitions of size n pyramidal planar partition.

1, 2, 9, 96, 2498, 161422, 26217833, 10794429504

Offset: 0

Author

Franklin T. Adams-Watters, Mar 14 2006

Keywords

• more
• nonn

Comments

This is a 2-dimensional analog of the Catalan numbers C_n (A000108). The number of subpartitions of the triangular partition [n,n-1,...,1] is C_{n+1}. The planar partition having its subpartitions counted is:

n n-1 ... 2 1

n-1 n-2 ... 1

... ...

2 1

1

Examples

			The 9 planar subpartitions of [2,1|1] are [], [1], [2], [1,1], [1|1], [2,1], [2|1], [1,1|1] and [2,1|1] itself, so a(2)=9. (Here "," separates values on the same line and "|" separates lines.)
		

Links

• Oleg Lazarev, Matt Mizuhara, Ben Reid, Some Results in Partitions, Plane Partitions, and Multipartitions

Crossrefs

Cf. A115728, A115729, A000219, A000108, A008793.