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 A330058 Number of non-isomorphic multiset partitions of weight n with at least one endpoint. 8
 0, 1, 2, 7, 21, 68, 214, 706, 2335, 7968, 27661 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. An endpoint is a vertex appearing only once (degree 1). Also the number of non-isomorphic multiset partitions of weight n with at least one singleton. LINKS Wikipedia, Degree (graph theory) EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(4) = 21 multiset partitions:   {1}  {12}    {122}      {1222}        {1}{2}  {123}      {1233}                {1}{22}    {1234}                {1}{23}    {1}{222}                {2}{12}    {12}{22}                {1}{2}{2}  {1}{233}                {1}{2}{3}  {12}{33}                           {1}{234}                           {12}{34}                           {13}{23}                           {2}{122}                           {3}{123}                           {1}{1}{23}                           {1}{2}{22}                           {1}{2}{33}                           {1}{2}{34}                           {1}{3}{23}                           {2}{2}{12}                           {1}{2}{2}{2}                           {1}{2}{3}{3}                           {1}{2}{3}{4} CROSSREFS The case of set-systems is A330053 (singletons) or A330052 (endpoints). The complement is counted by A302545. Cf. A007716, A283877, A306005, A330054, A330055, A330059. Sequence in context: A344500 A186240 A274203 * A220726 A347302 A127540 Adjacent sequences:  A330055 A330056 A330057 * A330059 A330060 A330061 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 30 2019 STATUS approved

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)