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 A318565 Number of multiset partitions of multiset partitions of strongly normal multisets of size n. 18
 1, 6, 27, 169, 1029, 7817, 61006, 547537, 5202009, 54506262, 606311524, 7299051826, 92985064466, 1264720212352, 18137495642192, 275078184766323, 4379514178076452, 73235806332442156, 1280229713195027792, 23381809052104639236, 444740694108284116235, 8801030741502964613534 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A multiset is normal if it spans an initial interval of positive integers, and strongly normal if in addition it has weakly decreasing multiplicities. LINKS EXAMPLE The a(2) = 6 multiset partitions of multiset partitions:   {{{1,1}}}   {{{1,2}}}   {{{1},{1}}}   {{{1},{2}}}   {{{1}},{{1}}}   {{{1}},{{2}}} 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]; Table[Sum[Length[mps[m]], {m, Join@@mps/@strnorm[n]}], {n, 6}] PROG (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 CROSSREFS 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 KEYWORD nonn AUTHOR Gus Wiseman, Aug 29 2018 EXTENSIONS Terms a(9) and beyond from Andrew Howroyd, Dec 30 2020 STATUS approved

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Last modified May 22 09:50 EDT 2022. Contains 353949 sequences. (Running on oeis4.)