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A318564
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Number of multiset partitions of multiset partitions of normal multisets of size n.
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16
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1, 6, 36, 274, 2408, 24440, 279172, 3542798, 49354816, 747851112, 12231881948, 214593346534, 4016624367288, 79843503990710, 1678916979373760, 37215518578700028, 866953456654946948, 21167221410812128266, 540346299720320080828, 14390314687100383124540, 399023209689817997883900
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OFFSET
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1,2
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COMMENTS
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A multiset is normal if it spans an initial interval of positive integers.
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LINKS
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EXAMPLE
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The a(2) = 6 multiset partitions of multiset partitions:
{{{1,1}}}
{{{1,2}}}
{{{1},{1}}}
{{{1},{2}}}
{{{1}},{{1}}}
{{{1}},{{2}}}
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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]]]];
allnorm[n_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]];
Table[Sum[Length[mps[m]], {m, Join@@mps/@allnorm[n]}], {n, 6}]
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PROG
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(PARI) \\ See links in A339645 for combinatorial species functions.
seq(n)={my(A=symGroupSeries(n)); NormalLabelingsSeq(sExp(sExp(A))-1)} \\ Andrew Howroyd, Jan 01 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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