OFFSET
0,8
EXAMPLE
The set partition {{1,3},{2},{4}} has two distinct block-sums {2,4} so is counted under T(4,2).
Triangle begins:
1
0 1
0 1 1
0 2 2 1
0 2 8 4 1
0 2 19 24 6 1
0 2 47 95 49 9 1
0 6 105 363 297 93 12 1
0 12 248 1292 1660 753 158 16 1
0 11 563 4649 8409 5591 1653 250 20 1
0 2 1414 15976 41264 38074 15590 3249 380 25 1
Row n = 4 counts the following set partitions:
. {{1,4},{2,3}} {{1},{2,3,4}} {{1},{2},{3,4}} {{1},{2},{3},{4}}
{{1,2,3,4}} {{1,2},{3},{4}} {{1},{2,3},{4}}
{{1,2},{3,4}} {{1},{2,4},{3}}
{{1,3},{2},{4}} {{1,4},{2},{3}}
{{1,3},{2,4}}
{{1,2,3},{4}}
{{1,2,4},{3}}
{{1,3,4},{2}}
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]& /@ sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[sps[Range[n]], Length[Union[Total/@#]]==k&]], {n, 0, 5}, {k, 0, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Apr 16 2024
STATUS
approved