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%I #5 Jan 29 2019 11:47:47
%S 1,1,3,8,27,82,310,1163
%N Number of non-isomorphic weight-n sets of non-overlapping sets of sets.
%C Also the number of non-isomorphic set partitions of set-systems of weight n.
%C All sets and multisets must be finite, and only the outermost may be empty.
%C The weight of an atom is 1, and the weight of a multiset is the sum of weights of its elements, counting multiplicity.
%e Non-isomorphic representatives of the a(1) = 1 through a(4) = 27 multiset partitions:
%e {{1}} {{12}} {{123}} {{1234}}
%e {{1}{2}} {{1}{12}} {{1}{123}}
%e {{1}}{{2}} {{1}{23}} {{12}{13}}
%e {{1}}{{12}} {{1}{234}}
%e {{1}}{{23}} {{12}{34}}
%e {{1}{2}{3}} {{1}}{{123}}
%e {{1}}{{2}{3}} {{1}{2}{12}}
%e {{1}}{{2}}{{3}} {{1}{2}{13}}
%e {{12}}{{13}}
%e {{1}}{{234}}
%e {{1}{2}{34}}
%e {{12}}{{34}}
%e {{1}}{{2}{12}}
%e {{12}}{{1}{2}}
%e {{1}}{{2}{13}}
%e {{12}}{{1}{3}}
%e {{1}}{{2}{34}}
%e {{1}{2}{3}{4}}
%e {{12}}{{3}{4}}
%e {{2}}{{1}{13}}
%e {{1}}{{2}}{{12}}
%e {{1}}{{2}}{{13}}
%e {{1}}{{2}}{{34}}
%e {{1}}{{2}{3}{4}}
%e {{1}{2}}{{3}{4}}
%e {{1}}{{2}}{{3}{4}}
%e {{1}}{{2}}{{3}}{{4}}
%Y Cf. A004111, A007716, A049311, A050326, A050343, A283877, A306186, A318566.
%Y Cf. A323787, A323788, A323789, A323790, A323791, A323792, A323793, A323794.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Jan 28 2019
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