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%I #9 May 31 2023 10:49:06
%S 1,0,0,0,1,4,24,96,412,1607,6348,24580,96334,378569,1508220,6079720,
%T 24879878,103335386,436032901,1869019800,8139613977,36008825317,
%U 161794412893,738167013847,3418757243139,16068569129711,76622168743677,370571105669576,1817199912384794
%N Number of non-isomorphic connected strict multiset partitions (sets of multisets) of weight n with empty intersection.
%C The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%H Andrew Howroyd, <a href="/A319793/b319793.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = A319557(n) - A316980(n) + A319077(n). - _Andrew Howroyd_, May 31 2023
%e Non-isomorphic representatives of the a(4) = 1 through a(5) = 4 multiset partitions:
%e 4: {{1},{2},{1,2}}
%e 5: {{1},{2},{1,2,2}}
%e {{1},{1,2},{2,2}}
%e {{2},{3},{1,2,3}}
%e {{2},{1,3},{2,3}}
%Y Cf. A007716, A007718, A056156, A281116, A283877, A316980, A317752, A317755, A317757, A319616.
%Y Cf. A319077, A319748, A319755, A319778, A319781, A319791.
%K nonn
%O 0,6
%A _Gus Wiseman_, Sep 27 2018
%E Terms a(11) and beyond from _Andrew Howroyd_, May 31 2023
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