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%I #6 Jan 28 2019 08:07:13
%S 1,1,3,9,33,113,474,1985
%N Number of non-isomorphic weight-n sets of sets of sets.
%C Non-isomorphic sets of sets are counted by A283877.
%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(3) = 9 sets of sets of sets:
%e {{1}} {{12}} {{123}}
%e {{1}{2}} {{1}{12}}
%e {{1}}{{2}} {{1}{23}}
%e {{1}}{{12}}
%e {{1}}{{23}}
%e {{1}{2}{3}}
%e {{1}}{{1}{2}}
%e {{1}}{{2}{3}}
%e {{1}}{{2}}{{3}}
%e Non-isomorphic representatives of the a(4) = 33 sets of sets of sets:
%e {{1234}} {{1}{123}} {{1}{2}{12}} {{1}}{{1}{12}}
%e {{1}{234}} {{12}{13}} {{1}}{{2}{12}}
%e {{12}{34}} {{1}}{{123}} {{12}}{{1}{2}}
%e {{1}}{{234}} {{1}{2}{13}} {{1}}{{2}}{{12}}
%e {{1}{2}{34}} {{12}}{{13}} {{1}}{{2}}{{1}{2}}
%e {{12}}{{34}} {{1}}{{1}{23}}
%e {{1}}{{2}{34}} {{1}}{{2}{13}}
%e {{1}{2}{3}{4}} {{12}}{{1}{3}}
%e {{12}}{{3}{4}} {{2}}{{1}{13}}
%e {{1}}{{2}}{{34}} {{1}}{{1}{2}{3}}
%e {{1}}{{2}{3}{4}} {{1}}{{2}}{{13}}
%e {{1}{2}}{{3}{4}} {{1}{2}}{{1}{3}}
%e {{1}}{{2}}{{3}{4}} {{1}}{{2}}{{1}{3}}
%e {{1}}{{2}}{{3}}{{4}}
%Y Cf. A004111, A007716, A049311, A050326, A050343, A283877, A306186, A316980, A318564, A318565, A318566, A318812.
%Y Cf. A323787, A323788, A323789, A323791, A323792, A323793, A323794, A323795.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Jan 27 2019
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