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 A322441 Number of pairs of set partitions of {1,...,n} where no block of one is a subset or equal to any block of the other. 9
 1, 0, 0, 0, 6, 60, 630, 9660, 192906 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS For any pair (X,Y) meeting the requirement, so does the pair (Y,X) which must be distinct from (X,Y), except for X = Y = {} when n = 0. Therefore all a(n) are even for n > 0. - M. F. Hasler, Dec 30 2020 LINKS EXAMPLE The a(4) = 6 pairs of set partitions:   {{1,2},{3,4}} and {{1,3},{2,4}},   {{1,2},{3,4}} and {{1,4},{2,3}},   {{1,3},{2,4}} and {{1,2},{3,4}},   {{1,3},{2,4}} and {{1,4},{2,3}},   {{1,4},{2,3}} and {{1,2},{3,4}},   {{1,4},{2,3}} and {{1,3},{2,4}}. MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; stabQ[u_]:=stabQ[u, SubsetQ]; stabQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}]; Table[Length[Select[Tuples[sps[Range[n]], 2], And[UnsameQ@@Join@@#, stabQ[Join@@#]]&]], {n, 6}] CROSSREFS Cf. A000110, A000258, A001247, A008277, A059849, A060639, A181939, A318393, A321760 (unlabeled version), A322435, A322442. Sequence in context: A136893 A090019 A186676 * A186674 A186672 A295503 Adjacent sequences:  A322438 A322439 A322440 * A322442 A322443 A322444 KEYWORD nonn,more AUTHOR Gus Wiseman, Dec 08 2018 STATUS approved

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Last modified May 15 18:17 EDT 2021. Contains 343920 sequences. (Running on oeis4.)