cp's OEIS Frontend

A322112 Number of non-isomorphic self-dual connected multiset partitions of weight n with no singletons and multiset density -1.

%I A322112 #5 Nov 27 2018 16:18:12
%S A322112 1,0,1,1,1,2,2,4,4,9,9
%N A322112 Number of non-isomorphic self-dual connected multiset partitions of weight n with no singletons and multiset density -1.
%C A322112 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 A322112 The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. A multiset partition is self-dual if it is isomorphic to its dual. For example, {{1,1},{1,2,2},{2,3,3}} is self-dual, as it is isomorphic to its dual {{1,1,2},{2,2,3},{3,3}}.
%C A322112 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 A322112 Non-isomorphic representatives of the a(2) = 1 through a(10) = 9 multiset partitions:
%e A322112   {{11}}  {{111}}  {{1111}}  {{11111}}    {{111111}}    {{1111111}}
%e A322112                              {{11}{122}}  {{22}{1122}}  {{111}{1222}}
%e A322112                                                         {{22}{11222}}
%e A322112                                                         {{11}{12}{233}}
%e A322112 .
%e A322112   {{11111111}}      {{111111111}}        {{1111111111}}
%e A322112   {{111}{11222}}    {{1111}{12222}}      {{1111}{112222}}
%e A322112   {{22}{112222}}    {{22}{1122222}}      {{22}{11222222}}
%e A322112   {{11}{122}{233}}  {{222}{111222}}      {{222}{1112222}}
%e A322112                     {{11}{11}{12233}}    {{111}{122}{2333}}
%e A322112                     {{11}{113}{2233}}    {{22}{113}{23333}}
%e A322112                     {{12}{111}{2333}}    {{22}{1133}{2233}}
%e A322112                     {{22}{113}{2333}}    {{33}{33}{112233}}
%e A322112                     {{12}{13}{22}{344}}  {{11}{14}{223}{344}}
%Y A322112 Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A316983, A321155, A321255, A322111.
%K A322112 nonn,more
%O A322112 0,6
%A A322112 _Gus Wiseman_, Nov 26 2018