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 A330668 Number of non-isomorphic balanced reduced multisystems of weight n whose leaves (which are multisets of atoms) are all sets. 6
 1, 1, 1, 3, 22, 204, 2953 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A balanced reduced multisystem is either a finite multiset, or a multiset partition with at least two parts, not all of which are singletons, of a balanced reduced multisystem. The weight of an atom is 1, while the weight of a multiset is the sum of weights of its elements. LINKS EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(4) = 22 multisystems:   {1}  {1,2}  {1,2,3}      {1,2,3,4}               {{1},{1,2}}  {{1},{1,2,3}}               {{1},{2,3}}  {{1,2},{1,2}}                            {{1,2},{1,3}}                            {{1},{2,3,4}}                            {{1,2},{3,4}}                            {{1},{1},{1,2}}                            {{1},{1},{2,3}}                            {{1},{2},{1,2}}                            {{1},{2},{1,3}}                            {{1},{2},{3,4}}                            {{{1}},{{1},{1,2}}}                            {{{1}},{{1},{2,3}}}                            {{{1,2}},{{1},{1}}}                            {{{1}},{{2},{1,2}}}                            {{{1,2}},{{1},{2}}}                            {{{1}},{{2},{1,3}}}                            {{{1,2}},{{1},{3}}}                            {{{1}},{{2},{3,4}}}                            {{{1,2}},{{3},{4}}}                            {{{2}},{{1},{1,3}}}                            {{{2,3}},{{1},{1}}} CROSSREFS The case with all atoms different is A318813. The version where the leaves are multisets is A330474. The tree version is A330626. The maximum-depth case is A330677. Unlabeled series-reduced rooted trees whose leaves are sets are A330624. Cf. A000311, A004114, A005121, A005804, A007716, A048816, A141268, A283877, A306186, A318812, A320154, A330470, A330628, A330663. Sequence in context: A098618 A207326 A006783 * A001409 A260154 A079489 Adjacent sequences:  A330665 A330666 A330667 * A330669 A330670 A330671 KEYWORD nonn,more AUTHOR Gus Wiseman, Dec 27 2019 STATUS approved

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Last modified November 24 20:34 EST 2020. Contains 338616 sequences. (Running on oeis4.)