A321231 - OEIS

%I #4 Nov 01 2018 11:38:00

%S 1,0,2,3,8,15,42,94,256,656,1807

%N Number of non-isomorphic connected weight-n multiset partitions with no singletons and multiset density -1.

%C 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.

%C The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

%e Non-isomorphic representatives of the a(2) = 2 through a(5) = 15 multiset partitions:

%e   {{1,1}}  {{1,1,1}}  {{1,1,1,1}}    {{1,1,1,1,1}}

%e   {{1,2}}  {{1,2,2}}  {{1,1,2,2}}    {{1,1,2,2,2}}

%e            {{1,2,3}}  {{1,2,2,2}}    {{1,2,2,2,2}}

%e                       {{1,2,3,3}}    {{1,2,2,3,3}}

%e                       {{1,2,3,4}}    {{1,2,3,3,3}}

%e                       {{1,1},{1,1}}  {{1,2,3,4,4}}

%e                       {{1,2},{2,2}}  {{1,2,3,4,5}}

%e                       {{1,3},{2,3}}  {{1,1},{1,1,1}}

%e                                      {{1,1},{1,2,2}}

%e                                      {{1,2},{2,2,2}}

%e                                      {{1,2},{2,3,3}}

%e                                      {{1,3},{2,3,3}}

%e                                      {{1,4},{2,3,4}}

%e                                      {{2,2},{1,2,2}}

%e                                      {{3,3},{1,2,3}}

%Y Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A317672, A318697, A321155, A321228, A321229.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Oct 31 2018