OFFSET
0,5
COMMENTS
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.
FORMULA
For n > 0, a(n) = A322441(n)/2.
EXAMPLE
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}}.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Antti Karttunen, Dec 10 2020
STATUS
approved