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 A320351 Number of connected multiset partitions of integer partitions of n. 4
 1, 1, 3, 5, 11, 18, 38, 66, 130, 237, 449, 823, 1538 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS EXAMPLE The a(1) = 1 through a(5) = 18 multiset partitions:   {{1}}  {{2}}      {{3}}          {{4}}              {{5}}          {{1,1}}    {{1,2}}        {{1,3}}            {{1,4}}          {{1},{1}}  {{1,1,1}}      {{2,2}}            {{2,3}}                     {{1},{1,1}}    {{1,1,2}}          {{1,1,3}}                     {{1},{1},{1}}  {{2},{2}}          {{1,2,2}}                                    {{1,1,1,1}}        {{1,1,1,2}}                                    {{1},{1,2}}        {{1},{1,3}}                                    {{1},{1,1,1}}      {{2},{1,2}}                                    {{1,1},{1,1}}      {{1,1,1,1,1}}                                    {{1},{1},{1,1}}    {{1},{1,1,2}}                                    {{1},{1},{1},{1}}  {{1,1},{1,2}}                                                       {{1},{1,1,1,1}}                                                       {{1,1},{1,1,1}}                                                       {{1},{1},{1,2}}                                                       {{1},{1},{1,1,1}}                                                       {{1},{1,1},{1,1}}                                                       {{1},{1},{1},{1,1}}                                                       {{1},{1},{1},{1},{1}} 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]]]]; csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; Table[Length[Select[Join@@mps/@IntegerPartitions[n], Length[csm[#]]==1&]], {n, 8}] CROSSREFS Cf. A001970, A007718, A048143, A056156, A258466, A261006, A293994, A319719, A320328, A320330, A320331, A320355, A320356. Sequence in context: A320789 A269628 A162891 * A319641 A306895 A198519 Adjacent sequences:  A320348 A320349 A320350 * A320352 A320353 A320354 KEYWORD nonn,more AUTHOR Gus Wiseman, Oct 11 2018 STATUS approved

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Last modified January 23 16:48 EST 2020. Contains 331173 sequences. (Running on oeis4.)