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 A330655 Number of balanced reduced multisystems of weight n whose atoms cover an initial interval of positive integers. 11
 1, 1, 2, 12, 138, 2652, 78106, 3256404, 182463296, 13219108288, 1202200963522, 134070195402644, 17989233145940910, 2858771262108762492, 530972857546678902490, 113965195745030648131036, 27991663753030583516229824, 7800669355870672032684666900, 2448021231611414334414904013956 (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. The weight of an atom is 1, while the weight of a multiset is the sum of weights of its elements. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 EXAMPLE The a(0) = 1 through a(3) = 12 multisystems:   {}  {1}  {1,1}  {1,1,1}            {1,2}  {1,1,2}                   {1,2,2}                   {1,2,3}                   {{1},{1,1}}                   {{1},{1,2}}                   {{1},{2,2}}                   {{1},{2,3}}                   {{2},{1,1}}                   {{2},{1,2}}                   {{2},{1,3}}                   {{3},{1,2}} MATHEMATICA allnorm[n_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]]; 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]]]]; totm[m_]:=Prepend[Join@@Table[totm[p], {p, Select[mps[m], 1

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Last modified July 27 23:16 EDT 2021. Contains 346316 sequences. (Running on oeis4.)