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 A321253 Number of non-isomorphic strict connected weight-n multiset partitions with multiset density -1. 5
 0, 1, 2, 5, 12, 28, 78, 202, 578, 1650, 4904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices. The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. LINKS EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(5) = 28 multiset partitions:   {{1}}  {{1,1}}  {{1,1,1}}    {{1,1,1,1}}      {{1,1,1,1,1}}          {{1,2}}  {{1,2,2}}    {{1,1,2,2}}      {{1,1,2,2,2}}                   {{1,2,3}}    {{1,2,2,2}}      {{1,2,2,2,2}}                   {{1},{1,1}}  {{1,2,3,3}}      {{1,2,2,3,3}}                   {{2},{1,2}}  {{1,2,3,4}}      {{1,2,3,3,3}}                                {{1},{1,1,1}}    {{1,2,3,4,4}}                                {{1},{1,2,2}}    {{1,2,3,4,5}}                                {{1,2},{2,2}}    {{1},{1,1,1,1}}                                {{1,3},{2,3}}    {{1,1},{1,1,1}}                                {{2},{1,2,2}}    {{1,1},{1,2,2}}                                {{3},{1,2,3}}    {{1},{1,2,2,2}}                                {{1},{2},{1,2}}  {{1,2},{2,2,2}}                                                 {{1,2},{2,3,3}}                                                 {{1,3},{2,3,3}}                                                 {{1,4},{2,3,4}}                                                 {{2},{1,1,2,2}}                                                 {{2},{1,2,2,2}}                                                 {{2},{1,2,3,3}}                                                 {{2,2},{1,2,2}}                                                 {{3},{1,2,3,3}}                                                 {{3,3},{1,2,3}}                                                 {{4},{1,2,3,4}}                                                 {{1},{1,2},{2,2}}                                                 {{1},{2},{1,2,2}}                                                 {{2},{1,2},{2,2}}                                                 {{2},{1,3},{2,3}}                                                 {{2},{3},{1,2,3}}                                                 {{3},{1,3},{2,3}} CROSSREFS Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A318697, A321155, A321194, A321228, A321229, A321254. Sequence in context: A291234 A238828 A162036 * A290073 A232534 A274594 Adjacent sequences:  A321250 A321251 A321252 * A321254 A321255 A321256 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 01 2018 STATUS approved

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Last modified July 22 16:39 EDT 2019. Contains 325224 sequences. (Running on oeis4.)