A119339 Triangle: number of exactly (m-1)-dimensional partitions of n, up to conjugacy, for n >= 1, m=n..1.
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 3, 1, 0, 1, 2, 5, 5, 1, 0, 1, 2, 6, 11, 7, 1, 0, 1, 2, 6, 16, 21, 11, 1, 0, 1, 2, 6, 18, 38, 39, 15, 1, 0, 1, 2, 6, 19, 51, 86, 73, 21, 1, 0, 1, 2, 6, 19, 57, 135, 193, 129, 28, 1, 0, 1, 2, 6, 19, 59, 170, 352, 420, 227, 39, 1, 0, 1, 2, 6, 19, 60, 186, 498
Offset: 0
Examples
Table starts: 1 1,0 1,1,0 1,2,1,0 1,2,3,1,0