A326513 Number of set partitions of {1..n} where each block has a different average.

1, 1, 2, 4, 12, 40, 154, 650, 3024, 15110, 81538, 468494, 2863340, 18481390, 125838194, 897725927, 6715102246, 52372397021, 425716871241, 3594451206166, 31509992921241, 285799247349838, 2682935185643622, 25990339824995969, 259777696236210943, 2673388551328088666

Offset: 0

Author

Gus Wiseman, Jul 11 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(4) = 12 set partitions:
  {{1}}  {{1,2}}    {{1,2,3}}      {{1,2,3,4}}
         {{1},{2}}  {{1},{2,3}}    {{1},{2,3,4}}
                    {{1,2},{3}}    {{1,2},{3,4}}
                    {{1},{2},{3}}  {{1,2,3},{4}}
                                   {{1,2,4},{3}}
                                   {{1,3},{2,4}}
                                   {{1,3,4},{2}}
                                   {{1},{2},{3,4}}
                                   {{1},{2,3},{4}}
                                   {{1,2},{3},{4}}
                                   {{1,4},{2},{3}}
                                   {{1},{2},{3},{4}}
		

Links

• Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

Crossrefs

Cf. A000110, A007837, A035470, A038041, A275780, A326512, A326516, A326521, A326537.

Programs

Mathematica

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Length[Select[sps[Range[n]],UnsameQ@@Mean/@#&]],{n,0,8}]

Extensions

a(12) from Alois P. Heinz, Jul 12 2019

a(13)-a(25) from Christian Sievers, Aug 20 2024