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.
1, 1, 2, 4, 10, 23, 62, 165, 475, 1400, 4334
Offset: 0
Examples
The multiset partition {{3},{1,3},{2,3}} has unique choice (3,1,2) so is counted under a(5).
Representatives of the a(1) = 1 through a(5) = 23 multiset partitions:
{1} {11} {111} {1111} {11111}
{1}{2} {1}{22} {1}{122} {11}{122}
{2}{12} {11}{22} {1}{1222}
{1}{2}{3} {12}{12} {11}{222}
{1}{222} {12}{122}
{12}{22} {1}{2222}
{2}{122} {12}{222}
{1}{2}{33} {2}{1122}
{1}{3}{23} {2}{1222}
{1}{2}{3}{4} {22}{122}
{1}{2}{233}
{1}{22}{33}
{1}{23}{23}
{1}{2}{333}
{1}{23}{33}
{1}{3}{233}
{2}{12}{33}
{2}{13}{23}
{2}{3}{123}
{3}{13}{23}
{1}{2}{3}{44}
{1}{2}{4}{34}
{1}{2}{3}{4}{5}
Crossrefs
Maximal sets of this type are counted by A370585.
Comments