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A318566 Number of non-isomorphic multiset partitions of multiset partitions of multisets of size n. 19
1, 6, 21, 104, 452, 2335, 11992 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

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}}}

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]]]];

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}]

CROSSREFS

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

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 29 2018

STATUS

approved

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Last modified October 19 21:17 EDT 2019. Contains 328229 sequences. (Running on oeis4.)