A327899 Number of set partitions of {1..n} with equal block sizes and equal block sums.

1, 1, 1, 1, 2, 1, 2, 1, 6, 3, 2, 1, 63, 1, 2, 317, 657, 1, 4333, 1, 9609

Offset: 0

Author

Gus Wiseman, Sep 29 2019

Keywords

• nonn
• more

Examples

			The a(8) = 6 set partitions:
     {{1,2,3,4,5,6,7,8}}
    {{1,2,7,8},{3,4,5,6}}
    {{1,3,6,8},{2,4,5,7}}
    {{1,4,5,8},{2,3,6,7}}
    {{1,4,6,7},{2,3,5,8}}
  {{1,8},{2,7},{3,6},{4,5}}
		

Links

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

Crossrefs

Set partitions with equal block-sizes are A038041.

Set partitions with equal block-sums are A035470.

Cf. A000110, A000258, A005651, A007837, A008277, A275780, A300335, A319189, A326512, A326513, A326515, A327908.

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]],And[SameQ@@Length/@#,SameQ@@Total/@#]&]],{n,0,8}]