%I #9 May 31 2023 10:49:09

%S 1,0,0,0,1,2,9,22,69,190,567,1640,5025,15404,49048,159074,531165,

%T 1813627,6352739,22759620,83443086,312612543,1196356133,4672620842,

%U 18615188819,75593464871,312729620542,1317267618429,5646454341658,24618309943464,109123789229297

%N Number of non-isomorphic connected set systems of weight n with empty intersection.

%C The weight of a set system is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

%H Andrew Howroyd, <a href="/A319792/b319792.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = A300913(n) - A283877(n) + A319751(n). - _Andrew Howroyd_, May 31 2023

%e Non-isomorphic representatives of the a(4) = 1 through a(6) = 9 connected set systems:

%e 4: {{1},{2},{1,2}}

%e 5: {{2},{3},{1,2,3}}

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

%e 6: {{1},{1,4},{2,3,4}}

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

%e {{3},{4},{1,2,3,4}}

%e {{3},{1,4},{2,3,4}}

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

%e {{1,3},{2,4},{3,4}}

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

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

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

%Y Cf. A007716, A007718, A049311, A056156, A281116, A283877, A300913, A305854, A316980, A317752, A317755, A317757.

%Y Cf. A319077, A319748, A319751, A319755, A319778, A319781, A319790.

%K nonn

%O 0,6

%A _Gus Wiseman_, Sep 27 2018

%E Terms a(11) and beyond from _Andrew Howroyd_, May 31 2023