OFFSET
1,3
EXAMPLE
The T(3,3,1) = 8 pairs of set partitions:
{{1},{2},{3}} {{1,2,3}}
{{1},{2,3}} {{1,2},{3}}
{{1},{2,3}} {{1,3},{2}}
{{1,2},{3}} {{1},{2,3}}
{{1,2},{3}} {{1,3},{2}}
{{1,3},{2}} {{1},{2,3}}
{{1,3},{2}} {{1,2},{3}}
{{1,2,3}} {{1},{2},{3}}
Tetrangle begins:
1 1 1 1 1
2 1 6 3 14 7 30 15
8 6 1 48 36 6 200 150 25
56 44 12 1 560 440 120 10
552 440 140 20 1
MATHEMATICA
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
spmeet[a_, b_]:=DeleteCases[Union@@Outer[Intersection, a, b, 1], {}]; spmeet[a_, b_, c__]:=spmeet[spmeet[a, b], c];
Table[Length[Select[Tuples[sps[Range[n]], 2], And[Length[spmeet@@#]==k, Length[csm[Union@@#]]==j]&]], {n, 6}, {k, n}, {j, k}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Aug 25 2018
STATUS
approved