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A318565
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Number of multiset partitions of multiset partitions of strongly normal multisets of size n.
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18
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1, 6, 27, 169, 1029, 7817, 61006, 547537, 5202009, 54506262, 606311524, 7299051826, 92985064466, 1264720212352, 18137495642192, 275078184766323, 4379514178076452, 73235806332442156, 1280229713195027792, 23381809052104639236, 444740694108284116235, 8801030741502964613534
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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, and strongly normal if in addition it has weakly decreasing multiplicities.
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LINKS
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Table of n, a(n) for n=1..22.
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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]]]];
strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];
Table[Sum[Length[mps[m]], {m, Join@@mps/@strnorm[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)); StronglyNormalLabelingsSeq(sExp(sExp(A))-1)} \\ Andrew Howroyd, Dec 30 2020
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CROSSREFS
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Cf. A001970, A007716, A050336, A255906, A269134, A317533, A317791, A318564, A318566.
Sequence in context: A117336 A202766 A144013 * A092854 A223557 A289022
Adjacent sequences: A318562 A318563 A318564 * A318566 A318567 A318568
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Aug 29 2018
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EXTENSIONS
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Terms a(9) and beyond from Andrew Howroyd, Dec 30 2020
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STATUS
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approved
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