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

1,9

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.

Links

Table of n, a(n) for n=1..84.

Formula

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

Example

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.

Sequence in context: A332670 A118344 A343138 * A267109 A341524 A175804

Adjacent sequences: A119267 A119268 A119269 * A119271 A119272 A119273

Keyword

nonn,tabl

Author

Franklin T. Adams-Watters, May 11 2006

Extensions

More terms from Max Alekseyev, May 15 2006

Status

approved