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 A330475 Number of balanced reduced multisystems whose atoms constitute a strongly normal multiset of size n. 13
 1, 1, 2, 9, 85, 1143, 25270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A balanced reduced multisystem is either a finite multiset, or a multiset partition with at least two parts, not all of which are singletons, of a balanced reduced multisystem. A finite multiset is strongly normal if it covers an initial interval of positive integers with weakly decreasing multiplicities. LINKS EXAMPLE The a(0) = 1 through a(3) = 9 multisystems:   {}  {1}  {1,1}  {1,1,1}            {1,2}  {1,1,2}                   {1,2,3}                   {{1},{1,1}}                   {{1},{1,2}}                   {{1},{2,3}}                   {{2},{1,1}}                   {{2},{1,3}}                   {{3},{1,2}} 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]; totm[m_]:=Prepend[Join@@Table[totm[p], {p, Select[mps[m], 1

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Last modified July 27 15:29 EDT 2021. Contains 346307 sequences. (Running on oeis4.)