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Number of non-isomorphic weight-n sets of set-systems with distinct multiset unions.
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%I #7 Feb 28 2020 12:55:01

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

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

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

%C 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.

%e Non-isomorphic representatives of the a(1) = 1 through a(3) = 9 sets:

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

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

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

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

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

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

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

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

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

%Y Non-isomorphic sets of sets are A283877.

%Y Non-isomorphic sets of sets of sets are A323790.

%Y Non-isomorphic set partitions of set-systems are A323795.

%Y Cf. A089259, A141268, A271619, A279375, A279785, A306186, A316980, A317533, A318564, A318565, A318566, A330459, A330472.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Dec 26 2019