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A318566
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Number of non-isomorphic multiset partitions of multiset partitions of multisets of size n.
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23
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1, 6, 21, 104, 452, 2335, 11992, 66810, 385101, 2336352, 14738380, 96831730, 659809115, 4657075074, 33974259046, 255781455848, 1984239830571, 15839628564349, 129951186405574, 1094486382191624, 9453318070371926, 83654146992936350, 757769011659766015, 7020652591448497490
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..24.
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EXAMPLE
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Non-isomorphic representatives of the a(3) = 21 multiset partitions of multiset partitions:
{{{1,1,1}}}
{{{1,1,2}}}
{{{1,2,3}}}
{{{1},{1,1}}}
{{{1},{1,2}}}
{{{1},{2,3}}}
{{{2},{1,1}}}
{{{1},{1},{1}}}
{{{1},{1},{2}}}
{{{1},{2},{3}}}
{{{1}},{{1,1}}}
{{{1}},{{1,2}}}
{{{1}},{{2,3}}}
{{{2}},{{1,1}}}
{{{1}},{{1},{1}}}
{{{1}},{{1},{2}}}
{{{1}},{{2},{3}}}
{{{2}},{{1},{1}}}
{{{1}},{{1}},{{1}}}
{{{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];
dubnorm[m_]:=First[Union[Table[Map[Sort, m/.Rule@@@Table[{Union[Flatten[m]][[i]], Union[Flatten[m]][[perm[[i]]]]}, {i, Length[perm]}], {0, 2}], {perm, Permutations[Union[Flatten[m]]]}]]];
Table[Length[Union[dubnorm/@Join@@mps/@Join@@mps/@strnorm[n]]], {n, 5}]
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PROG
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(PARI) \\ See links in A339645 for combinatorial species functions.
seq(n)={my(A=sExp(symGroupSeries(n))); NumUnlabeledObjsSeq(sCartProd(A, sExp(A)-1))} \\ Andrew Howroyd, Dec 30 2020
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CROSSREFS
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Cf. A001970, A007716, A050336, A050338, A255906, A269134, A317533, A317791, A318564, A318565.
Sequence in context: A012662 A012418 A203295 * A083558 A060843 A026650
Adjacent sequences: A318563 A318564 A318565 * A318567 A318568 A318569
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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(8) and beyond from Andrew Howroyd, Dec 30 2020
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STATUS
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approved
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