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 A330726 Number of balanced reduced multisystems of maximum depth whose atoms are positive integers summing to n. 2
 1, 1, 2, 3, 7, 17, 54, 199, 869, 4341, 24514, 154187 (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. LINKS EXAMPLE The a(1) = 1 through a(5) = 17 multisystems (commas elided): {1} {2} {3} {4} {5} {11} {12} {22} {23} {{1}{11}} {13} {14} {{1}{12}} {{1}{13}} {{2}{11}} {{1}{22}} {{{1}}{{1}{11}}} {{2}{12}} {{{11}}{{1}{1}}} {{3}{11}} {{{1}}{{1}{12}}} {{{11}}{{1}{2}}} {{{1}}{{2}{11}}} {{{12}}{{1}{1}}} {{{2}}{{1}{11}}} {{{{1}}}{{{1}}{{1}{11}}}} {{{{1}}}{{{11}}{{1}{1}}}} {{{{1}{1}}}{{{1}}{{11}}}} {{{{1}{11}}}{{{1}}{{1}}}} {{{{11}}}{{{1}}{{1}{1}}}} 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]]]]; totm[m_]:=Prepend[Join@@Table[totm[p], {p, Select[mps[m], 1

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Last modified February 1 04:51 EST 2023. Contains 359981 sequences. (Running on oeis4.)