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Number of non-isomorphic multiset partitions of strict multiset partitions of weight n.
17

%I #5 Jan 28 2019 08:06:40

%S 1,1,4,14,56,219,1001,4588

%N Number of non-isomorphic multiset partitions of strict multiset partitions of weight n.

%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) = 14 multiset partitions:

%e {{1}} {{11}} {{111}}

%e {{12}} {{112}}

%e {{1}{2}} {{123}}

%e {{1}}{{2}} {{1}{11}}

%e {{1}{12}}

%e {{1}{23}}

%e {{2}{11}}

%e {{1}}{{11}}

%e {{1}}{{12}}

%e {{1}}{{23}}

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

%e {{2}}{{11}}

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

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

%Y Cf. A002846, A005121, A007716, A050343, A213427, A269134, A283877, A306186, A316980, A317791, A318564, A318565, A318566, A318812.

%Y Cf. A323788, A323789, A323790, A323791, A323792, A323793, A323794, A323795.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Jan 27 2019