A119270 Triangle: number of exactly (m-1)-dimensional partitions of n, up to conjugacy, for n >= 1, m >= 0.

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 0, 1, 5, 5, 2, 1, 0, 1, 7, 11, 6, 2, 1, 0, 1, 11, 21, 16, 6, 2, 1, 0, 1, 15, 39, 38, 18, 6, 2, 1, 0, 1, 21, 73, 86, 51, 19, 6, 2, 1, 0, 1, 28, 129, 193, 135, 57, 19, 6, 2, 1, 0, 1, 39, 227, 420, 352, 170, 59, 19, 6, 2, 1, 0, 1, 51, 390, 890, 894

Offset: 1

Author

Franklin T. Adams-Watters, May 11 2006

Keywords

• nonn
• tabl

Comments

The partition of 1 is considered to be dimension -1 by convention.

Partitions are considered as generalized Ferrers diagrams; any permutation of the axes produces a conjugate.

Examples

			Table starts:
1
0,1
0,1,1
0,1,2,1
0,1,3,2,1
		

Crossrefs

Cf. A119269, A119271.

Reversed triangle is A119339. Columns stabilize to A118364.

Formula

a(n,m) = A119269(n,m)-A119269(n,m-1).

Extensions

More terms from Max Alekseyev, May 15 2006