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 A318389 Regular triangle where T(n,k) is the number of pairs of set partitions of {1,...,n} with meet {{1},...,{n}} and join of length k. 10
 1, 2, 1, 8, 6, 1, 56, 44, 12, 1, 552, 440, 140, 20, 1, 7202, 5632, 1920, 340, 30, 1, 118456, 89278, 31192, 6160, 700, 42, 1, 2369922, 1708016, 595448, 124432, 16240, 1288, 56, 1, 56230544, 38592786, 13214672, 2830632, 400512, 37296, 2184, 72, 1, 1552048082 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE The T(3,2) = 6 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},{2},{3}}    {{1,3},{2}}  {{1},{2},{3}} Triangle begins:      1      2    1      8    6    1     56   44   12    1    552  440  140   20    1   7202 5632 1920  340   30    1 MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; 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]]]]]]]]]; 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[Max@@Length/@spmeet@@#==1, Length[csm[Union@@#]]==k]&]], {n, 5}, {k, n}] CROSSREFS Row sums are A059849. First column is A181939. Cf. A000110, A000258, A001247, A008277, A048994, A060639, A318390, A318391, A318392, A318393. Sequence in context: A114193 A231846 A039683 * A108084 A108085 A305860 Adjacent sequences:  A318386 A318387 A318388 * A318390 A318391 A318392 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Aug 25 2018 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)