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%I #6 Jan 28 2019 08:06:47
%S 1,1,5,19,88,391,1995,10281
%N Number of non-isomorphic weight-n sets of multisets of multisets.
%C Also the number of non-isomorphic strict multiset partitions of multiset partitions 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(3) = 19 multiset partitions:
%e {{1}} {{11}} {{111}}
%e {{12}} {{112}}
%e {{1}{1}} {{123}}
%e {{1}{2}} {{1}{11}}
%e {{1}}{{2}} {{1}{12}}
%e {{1}{23}}
%e {{2}{11}}
%e {{1}}{{11}}
%e {{1}{1}{1}}
%e {{1}}{{12}}
%e {{1}{1}{2}}
%e {{1}}{{23}}
%e {{1}{2}{3}}
%e {{2}}{{11}}
%e {{1}}{{1}{1}}
%e {{1}}{{1}{2}}
%e {{1}}{{2}{3}}
%e {{2}}{{1}{1}}
%e {{1}}{{2}}{{3}}
%Y Cf. A005121, A007716, A049311, A050343, A283877, A306186, A316980, A317791, A318564, A318565, A318566, A318812.
%Y Cf. A323787, A323789, A323790, A323791, A323792, A323793, A323794, A323795.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Jan 27 2019
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