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A317755
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Number of multiset partitions of strongly normal multisets of size n such that the blocks have empty intersection.
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22
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0, 1, 6, 30, 130, 629, 2930, 15019, 78224, 438626, 2548481
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OFFSET
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1,3
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COMMENTS
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A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities.
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LINKS
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EXAMPLE
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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}}
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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