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%I #9 May 31 2023 10:49:17
%S 1,0,0,0,1,5,32,134,588,2335,9335,36506,144263,571238,2291894,9300462,
%T 38303796,160062325,679333926,2927951665,12817221628,56974693933,
%U 257132512297,1177882648846,5475237760563,25818721638720,123473772356785,598687942799298,2942344764127039
%N Number of non-isomorphic connected multiset partitions 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="/A319790/b319790.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = A007718(n) - A007716(n) + A317757(n). - _Andrew Howroyd_, May 31 2023
%e Non-isomorphic representatives of the a(4) = 1 through a(5) = 5 connected 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}}
%e {{1},{2},{2},{1,2}}
%Y Cf. A007716, A007718, A049311, A056156, A283877, A317752, A317755, A317757.
%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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