A339626 a(n) = A322437(A002110(n)).

0, 0, 0, 0, 3, 30, 315, 4830, 96453, 2296350

Offset: 0

Author

Antti Karttunen, Dec 10 2020

Keywords

• nonn
• more

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.

Examples

			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}}.
		

Crossrefs

Cf. A002110, A322437, A322441.

Programs

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 *)

Formula

For n > 0, a(n) = A322441(n)/2.