A323790 -id:A323790 - cp's OEIS frontend

A330464 Number of non-isomorphic weight-n sets of set-systems with distinct multiset unions.

1, 1, 3, 9, 32, 111, 463, 1942

Offset: 0

Gus Wiseman, Dec 26 2019

A set-system is a finite set of finite nonempty sets of positive integers.

As an alternative description, a(n) is the number of non-isomorphic sets of sets of sets with n leaves where the inner sets of sets all have different multiset unions.

			Non-isomorphic representatives of the a(1) = 1 through a(3) = 9 sets:
  {}  {{{1}}}  {{{1,2}}}      {{{1,2,3}}}
               {{{1},{2}}}    {{{1},{1,2}}}
               {{{1}},{{2}}}  {{{1},{2,3}}}
                              {{{1}},{{1,2}}}
                              {{{1}},{{2,3}}}
                              {{{1},{2},{3}}}
                              {{{1}},{{1},{2}}}
                              {{{1}},{{2},{3}}}
                              {{{1}},{{2}},{{3}}}

Non-isomorphic sets of sets are A283877.
Non-isomorphic sets of sets of sets are A323790.
Non-isomorphic set partitions of set-systems are A323795.
Cf. A089259, A141268, A271619, A279375, A279785, A306186, A316980, A317533, A318564, A318565, A318566, A330459, A330472.

cp's OEIS Frontend

A330464 Number of non-isomorphic weight-n sets of set-systems with distinct multiset unions.

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