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OFFSET
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0,5
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COMMENTS
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For n > 0, a(n) gives the number of unordered pairs of set partitions of {1,...,n} where no block of the other is a subset (or equal) to any block of the other. See A322441.
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LINKS
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FORMULA
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EXAMPLE
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The a(4) = 3 such (unordered) pairs of set partitions of {1,2,3,4} are:
{{1,2},{3,4}}|{{1,3},{2,4}}
{{1,2},{3,4}}|{{1,4},{2,3}}
{{1,3},{2,4}}|{{1,4},{2,3}}.
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MATHEMATICA
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Block[{f}, f[n_] := If[n <= 1, {{}}, Join @@ Table[Map[Prepend[#, d] &, Select[f[n/d], Min @@ # >= d &]], {d, Rest[Divisors[n]]}]]; Map[Length[Select[Subsets[f[#], {2}], And[! Or @@ Divisible @@@ #, ! Or @@ Divisible @@@ Reverse /@ #] &@ Tuples[#] &]] &, FoldList[Times, 1, Prime@ Range@ 7]] ] (* Michael De Vlieger, Dec 10 2020, after Gus Wiseman at A322437 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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