OFFSET
0,3
COMMENTS
Number of ways to fill a (not necessarily square) matrix with the parts of an integer partition of n so that the rows are weakly decreasing and the columns are strictly decreasing.
EXAMPLE
The a(6) = 15 matrices:
[6] [51] [42] [411] [33] [321] [3111] [222] [2211] [21111] [111111]
.
[5] [4] [22]
[1] [2] [11]
.
[3]
[2]
[1]
MATHEMATICA
Table[Sum[Length[Select[Union[Tuples[IntegerPartitions[#, {k}]&/@ptn]], And@@(OrderedQ[#, Greater]&/@Transpose[#])&]], {ptn, IntegerPartitions[n]}, {k, Min[ptn]}], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 16 2019
STATUS
approved