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%I #8 Feb 23 2019 10:11:34
%S 1,1,5,15,65,240,1090,4845
%N Number of non-isomorphic weight-n multisets of multisets of sets.
%C Also the number of non-isomorphic multiset partitions of set multipartitions 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) = 15 multiset partitions:
%e {{1}} {{12}} {{123}}
%e {{1}{1}} {{1}{12}}
%e {{1}{2}} {{1}{23}}
%e {{1}}{{1}} {{1}{1}{1}}
%e {{1}}{{2}} {{1}}{{12}}
%e {{1}{1}{2}}
%e {{1}}{{23}}
%e {{1}{2}{3}}
%e {{1}}{{1}{1}}
%e {{1}}{{1}{2}}
%e {{1}}{{2}{3}}
%e {{2}}{{1}{1}}
%e {{1}}{{1}}{{1}}
%e {{1}}{{1}}{{2}}
%e {{1}}{{2}}{{3}}
%Y Cf. A007716, A049311, A283877, A306186, A316980, A318565, A318566.
%Y Cf. A323787, A323788, A323789, A323790, A323791, A323792, A323794, A323795.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Jan 27 2019
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