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%I #5 Sep 28 2018 15:24:05
%S 1,0,0,1,3,9,21,48,103,214,436,863,1689
%N Number of multiset partitions of integer partitions of n with empty intersection. Number of relatively prime factorizations of Heinz numbers of integer partitions of n.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%e The a(3) = 1 through a(5) = 9 multiset partitions:
%e 3: {{1},{2}}
%e 4: {{1},{3}}
%e {{2},{1,1}}
%e {{1},{1},{2}}
%e 5: {{1},{4}}
%e {{2},{3}}
%e {{3},{1,1}}
%e {{1},{2,2}}
%e {{1},{1},{3}}
%e {{1},{2},{2}}
%e {{2},{1,1,1}}
%e {{1},{2},{1,1}}
%e {{1},{1},{1},{2}}
%Y Cf. A007716, A049311, A281116, A283877, A316980, A317752, A317755, A317757, A318715.
%Y Cf. A319775, A319779, A319778, A319783.
%K nonn,more
%O 0,5
%A _Gus Wiseman_, Sep 27 2018
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