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 A320449 Number of antichains of sets whose multiset union is an integer partition of n. 8
 1, 1, 2, 4, 6, 9, 18, 24, 39, 58, 92, 131, 206 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS EXAMPLE The a(1) = 1 through a(7) = 24 antichains:   {{1}}  {{2}}      {{3}}          {{4}}              {{5}}          {{1},{1}}  {{1,2}}        {{1,3}}            {{1,4}}                     {{1},{2}}      {{1},{3}}          {{2,3}}                     {{1},{1},{1}}  {{2},{2}}          {{1},{4}}                                    {{1},{1},{2}}      {{2},{3}}                                    {{1},{1},{1},{1}}  {{1},{1},{3}}                                                       {{1},{2},{2}}                                                       {{1},{1},{1},{2}}                                                       {{1},{1},{1},{1},{1}} .   {{6}}                      {{7}}   {{1,5}}                    {{1,6}}   {{2,4}}                    {{2,5}}   {{1,2,3}}                  {{3,4}}   {{1},{5}}                  {{1,2,4}}   {{2},{4}}                  {{1},{6}}   {{3},{3}}                  {{2},{5}}   {{1},{2,3}}                {{3},{4}}   {{2},{1,3}}                {{1},{2,4}}   {{3},{1,2}}                {{2},{1,4}}   {{1},{1},{4}}              {{4},{1,2}}   {{1,2},{1,2}}              {{1},{1},{5}}   {{1},{2},{3}}              {{1,2},{1,3}}   {{2},{2},{2}}              {{1},{2},{4}}   {{1},{1},{1},{3}}          {{1},{3},{3}}   {{1},{1},{2},{2}}          {{2},{2},{3}}   {{1},{1},{1},{1},{2}}      {{1},{1},{2,3}}   {{1},{1},{1},{1},{1},{1}}  {{1},{1},{1},{4}}                              {{1},{1},{2},{3}}                              {{1},{2},{2},{2}}                              {{1},{1},{1},{1},{3}}                              {{1},{1},{1},{2},{2}}                              {{1},{1},{1},{1},{1},{2}}                              {{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]]]]; submultisetQ[M_, N_]:=Or[Length[M]==0, MatchQ[{Sort[List@@M], Sort[List@@N]}, {{x_, Z___}, {___, x_, W___}}/; submultisetQ[{Z}, {W}]]]; antiQ[s_]:=Select[Tuples[s, 2], And[UnsameQ@@#, submultisetQ@@#]&]=={}; Table[Length[Select[Join@@mps/@IntegerPartitions[n], And[And@@UnsameQ@@@#, antiQ[#]]&]], {n, 10}] CROSSREFS Cf. A001970, A089259, A258466, A319719, A319721, A320328, A320353, A320355, A320356. Sequence in context: A244470 A098787 A164138 * A263434 A192079 A079143 Adjacent sequences:  A320446 A320447 A320448 * A320450 A320451 A320452 KEYWORD nonn,more AUTHOR Gus Wiseman, Oct 12 2018 STATUS approved

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Last modified April 1 02:15 EDT 2020. Contains 333153 sequences. (Running on oeis4.)