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 A340600 Number of non-isomorphic balanced multiset partitions of weight n. 13
 1, 1, 0, 4, 7, 16, 52, 206, 444, 1624, 5462 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS We define a multiset partition to be balanced if it has exactly as many parts as the greatest size of a part. LINKS EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(5) = 16 multiset partitions (empty column indicated by dot):   {{1}}  .  {{1},{1,1}}  {{1,1},{1,1}}  {{1},{1},{1,1,1}}             {{1},{2,2}}  {{1,1},{2,2}}  {{1},{1},{1,2,2}}             {{1},{2,3}}  {{1,2},{1,2}}  {{1},{1},{2,2,2}}             {{2},{1,2}}  {{1,2},{2,2}}  {{1},{1},{2,3,3}}                          {{1,2},{3,3}}  {{1},{1},{2,3,4}}                          {{1,2},{3,4}}  {{1},{2},{1,2,2}}                          {{1,3},{2,3}}  {{1},{2},{2,2,2}}                                         {{1},{2},{2,3,3}}                                         {{1},{2},{3,3,3}}                                         {{1},{2},{3,4,4}}                                         {{1},{2},{3,4,5}}                                         {{1},{3},{2,3,3}}                                         {{1},{4},{2,3,4}}                                         {{2},{2},{1,2,2}}                                         {{2},{3},{1,2,3}}                                         {{3},{3},{1,2,3}} CROSSREFS The version for partitions is A047993. The co-balanced version is A319616. The cross-balanced version is A340651. The twice-balanced version is A340652. The version for factorizations is A340653. A007716 counts non-isomorphic multiset partitions. A007718 counts non-isomorphic connected multiset partitions. A316980 counts non-isomorphic strict multiset partitions. Other balance-related sequences: - A098124 counts balanced compositions. - A106529 lists balanced numbers. - A340596 counts co-balanced factorizations. - A340597 lists numbers with an alt-balanced factorization. - A340598 counts balanced set partitions. - A340599 counts alt-balanced factorizations. Cf. A001055, A006141, A007717, A316983, A320663, A324522, A340654, A340655. Sequence in context: A097661 A182561 A246915 * A013625 A182929 A124402 Adjacent sequences:  A340597 A340598 A340599 * A340601 A340602 A340603 KEYWORD nonn,more AUTHOR Gus Wiseman, Feb 05 2021 STATUS approved

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Last modified June 20 06:56 EDT 2021. Contains 345157 sequences. (Running on oeis4.)