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A330058 Number of non-isomorphic multiset partitions of weight n with at least one endpoint.

%I A330058 #11 Jan 16 2023 04:33:36
%S A330058 0,1,2,7,21,68,214,706,2335,7968,27661,98366,357212,1326169,5027377,
%T A330058 19459252,76850284,309531069,1270740646,5314727630,22633477157,
%U A330058 98096319485,432490992805,1938762984374,8832924638252,40882143931620,192148753444380,916747097916418
%N A330058 Number of non-isomorphic multiset partitions of weight n with at least one endpoint.
%C A330058 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%C A330058 An endpoint is a vertex appearing only once (degree 1).
%C A330058 Also the number of non-isomorphic multiset partitions of weight n with at least one singleton.
%H A330058 Andrew Howroyd, <a href="/A330058/b330058.txt">Table of n, a(n) for n = 0..50</a>
%H A330058 Wikipedia, <a href="https://en.wikipedia.org/wiki/Degree_(graph_theory)">Degree (graph theory)</a>
%F A330058 a(n) = A007716(n) - A302545(n). - _Andrew Howroyd_, Jan 15 2023
%e A330058 Non-isomorphic representatives of the a(1) = 1 through a(4) = 21 multiset partitions:
%e A330058   {1}  {12}    {122}      {1222}
%e A330058        {1}{2}  {123}      {1233}
%e A330058                {1}{22}    {1234}
%e A330058                {1}{23}    {1}{222}
%e A330058                {2}{12}    {12}{22}
%e A330058                {1}{2}{2}  {1}{233}
%e A330058                {1}{2}{3}  {12}{33}
%e A330058                           {1}{234}
%e A330058                           {12}{34}
%e A330058                           {13}{23}
%e A330058                           {2}{122}
%e A330058                           {3}{123}
%e A330058                           {1}{1}{23}
%e A330058                           {1}{2}{22}
%e A330058                           {1}{2}{33}
%e A330058                           {1}{2}{34}
%e A330058                           {1}{3}{23}
%e A330058                           {2}{2}{12}
%e A330058                           {1}{2}{2}{2}
%e A330058                           {1}{2}{3}{3}
%e A330058                           {1}{2}{3}{4}
%Y A330058 The case of set-systems is A330053 (singletons) or A330052 (endpoints).
%Y A330058 The complement is counted by A302545.
%Y A330058 Cf. A007716, A283877, A306005, A330054, A330055, A330059.
%K A330058 nonn
%O A330058 0,3
%A A330058 _Gus Wiseman_, Nov 30 2019
%E A330058 Terms a(11) and beyond from _Andrew Howroyd_, Jan 15 2023