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 A318566 Number of non-isomorphic multiset partitions of multiset partitions of multisets of size n. 23
 1, 6, 21, 104, 452, 2335, 11992, 66810, 385101, 2336352, 14738380, 96831730, 659809115, 4657075074, 33974259046, 255781455848, 1984239830571, 15839628564349, 129951186405574, 1094486382191624, 9453318070371926, 83654146992936350, 757769011659766015, 7020652591448497490 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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}] PROG (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 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 AUTHOR Gus Wiseman, Aug 29 2018 EXTENSIONS Terms a(8) and beyond from Andrew Howroyd, Dec 30 2020 STATUS approved

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Last modified April 1 03:33 EDT 2023. Contains 361673 sequences. (Running on oeis4.)