A317755 Number of multiset partitions of strongly normal multisets of size n such that the blocks have empty intersection.

0, 1, 6, 30, 130, 629, 2930, 15019, 78224, 438626, 2548481

Offset: 1

Author

Gus Wiseman, Aug 06 2018

Keywords

• nonn
• more

Comments

A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities.

Examples

			The a(3) = 6 strongly normal multiset partitions with empty intersection:
  {{2},{1,1}}
  {{1},{2,3}}
  {{2},{1,3}}
  {{3},{1,2}}
  {{1},{1},{2}}
  {{1},{2},{3}}
		

Crossrefs

Cf. A007716, A035310, A255906, A317073, A281116, A317077, A317078, A317532, A317533.

Cf. A317748, A317751, A317752, A317757, A317775.

Programs

Mathematica

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
strnorm[n_]:=Flatten[MapIndexed[Table[#2,{#1}]&,#]]&/@IntegerPartitions[n];
Table[Length[Join@@Table[Select[mps[m],Intersection@@#=={}&],{m,strnorm[n]}]],{n,6}]

Extensions

a(10)-a(11) from Robert Price, May 08 2021