cp's OEIS Frontend

A370646 Number of non-isomorphic multiset partitions of weight n such that only one set can be obtained by choosing a different element of each block.

%I A370646 #7 Mar 12 2024 16:33:25
%S A370646 1,1,2,4,10,23,62,165,475,1400,4334
%N A370646 Number of non-isomorphic multiset partitions of weight n such that only one set can be obtained by choosing a different element of each block.
%C A370646 A multiset partition is a finite multiset of finite nonempty multisets. The weight of a multiset partition is the sum of cardinalities of its elements.
%e A370646 The multiset partition {{3},{1,3},{2,3}} has unique choice (3,1,2) so is counted under a(5).
%e A370646 Representatives of the a(1) = 1 through a(5) = 23 multiset partitions:
%e A370646   {1}  {11}    {111}      {1111}        {11111}
%e A370646        {1}{2}  {1}{22}    {1}{122}      {11}{122}
%e A370646                {2}{12}    {11}{22}      {1}{1222}
%e A370646                {1}{2}{3}  {12}{12}      {11}{222}
%e A370646                           {1}{222}      {12}{122}
%e A370646                           {12}{22}      {1}{2222}
%e A370646                           {2}{122}      {12}{222}
%e A370646                           {1}{2}{33}    {2}{1122}
%e A370646                           {1}{3}{23}    {2}{1222}
%e A370646                           {1}{2}{3}{4}  {22}{122}
%e A370646                                         {1}{2}{233}
%e A370646                                         {1}{22}{33}
%e A370646                                         {1}{23}{23}
%e A370646                                         {1}{2}{333}
%e A370646                                         {1}{23}{33}
%e A370646                                         {1}{3}{233}
%e A370646                                         {2}{12}{33}
%e A370646                                         {2}{13}{23}
%e A370646                                         {2}{3}{123}
%e A370646                                         {3}{13}{23}
%e A370646                                         {1}{2}{3}{44}
%e A370646                                         {1}{2}{4}{34}
%e A370646                                         {1}{2}{3}{4}{5}
%Y A370646 For existence we have A368098, complement A368097.
%Y A370646 Multisets of this type are ranked by A368101, see also A368100, A355529.
%Y A370646 Subsets of this type are counted by A370584, see also A370582, A370583.
%Y A370646 Maximal sets of this type are counted by A370585.
%Y A370646 Partitions of this type are counted by A370594, see also A370592, A370593.
%Y A370646 Subsets of this type are also counted by A370638, see also A370636, A370637.
%Y A370646 Factorizations of this type are A370645, see also A368414, A368413.
%Y A370646 Set-systems of this type are A370818, see also A367902, A367903.
%Y A370646 A000110 counts set partitions, non-isomorphic A000041.
%Y A370646 A001055 counts factorizations, strict A045778.
%Y A370646 A007716 counts non-isomorphic multiset partitions, connected A007718.
%Y A370646 Cf. A000612, A055621, A283877, A300913, A302545, A316983, A319616, A330223, A368095, A368412, A368422.
%K A370646 nonn,more
%O A370646 0,3
%A A370646 _Gus Wiseman_, Mar 12 2024