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 A322442 Number of pairs of set partitions of {1,...,n} where every block of one is a subset or superset of some block of the other. 9
 1, 1, 4, 25, 195, 1894, 22159, 303769 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS EXAMPLE The a(3) = 25 pairs of set partitions (these are actually all pairs of set partitions of {1,2,3}):   (1)(2)(3)|(1)(2)(3)   (1)(2)(3)|(1)(23)   (1)(2)(3)|(12)(3)   (1)(2)(3)|(13)(2)   (1)(2)(3)|(123)     (1)(23)|(1)(2)(3)     (1)(23)|(1)(23)     (1)(23)|(12)(3)     (1)(23)|(13)(2)     (1)(23)|(123)     (12)(3)|(1)(2)(3)     (12)(3)|(1)(23)     (12)(3)|(12)(3)     (12)(3)|(13)(2)     (12)(3)|(123)     (13)(2)|(1)(2)(3)     (13)(2)|(1)(23)     (13)(2)|(12)(3)     (13)(2)|(13)(2)     (13)(2)|(123)       (123)|(1)(2)(3)       (123)|(1)(23)       (123)|(12)(3)       (123)|(13)(2)       (123)|(123) Non-isomorphic representatives of the pairs of set partitions of {1,2,3,4} for which the condition fails:     (12)(34)|(13)(24)     (12)(34)|(1)(3)(24)   (1)(2)(34)|(13)(24) MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; costabQ[s_, t_]:=And@@Cases[s, x_:>Select[t, SubsetQ[x, #]||SubsetQ[#, x]&]!={}]; Table[Length[Select[Tuples[sps[Range[n]], 2], And[costabQ@@#, costabQ@@Reverse[#]]&]], {n, 5}] CROSSREFS Cf. A000110, A000258, A001247, A008277, A059849, A060639, A181939, A318393, A322435, A322437, A322439, A322440, A322441. Sequence in context: A199494 A171791 A060908 * A036449 A051500 A206179 Adjacent sequences:  A322439 A322440 A322441 * A322443 A322444 A322445 KEYWORD nonn,more AUTHOR Gus Wiseman, Dec 08 2018 STATUS approved

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Last modified May 11 03:49 EDT 2021. Contains 343784 sequences. (Running on oeis4.)