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%I #9 Aug 11 2019 12:23:55
%S 1,1,4,22,302,28630,216533404,5592325966377736
%N Number of unlabeled set-systems with {} that are closed under intersection and cover n vertices.
%F a(n) = A108800(n) - A108800(n-1) for n > 0. - _Andrew Howroyd_, Aug 10 2019
%e Non-isomorphic representatives of the a(0) = 1 through a(3) = 22 set-systems:
%e {{}} {{}{1}} {{}{12}} {{}{123}}
%e {{}{1}{2}} {{}{1}{23}}
%e {{}{2}{12}} {{}{3}{123}}
%e {{}{1}{2}{12}} {{}{1}{2}{3}}
%e {{}{23}{123}}
%e {{}{1}{3}{23}}
%e {{}{2}{3}{123}}
%e {{}{3}{13}{23}}
%e {{}{1}{23}{123}}
%e {{}{3}{23}{123}}
%e {{}{1}{2}{3}{23}}
%e {{}{1}{2}{3}{123}}
%e {{}{2}{3}{13}{23}}
%e {{}{1}{3}{23}{123}}
%e {{}{2}{3}{23}{123}}
%e {{}{3}{13}{23}{123}}
%e {{}{1}{2}{3}{13}{23}}
%e {{}{1}{2}{3}{23}{123}}
%e {{}{2}{3}{13}{23}{123}}
%e {{}{1}{2}{3}{12}{13}{23}}
%e {{}{1}{2}{3}{13}{23}{123}}
%e {{}{1}{2}{3}{12}{13}{23}{123}}
%Y The case also closed under union is A001930.
%Y The connected case (i.e., with maximum) is A108798.
%Y The same for union instead of intersection is (also) A108798.
%Y The non-covering case is A108800.
%Y The labeled case is A326881.
%Y Cf. A000798, A102894, A102895, A102897, A193674, A193675, A306445, A326875, A326878, A326880.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Jul 30 2019
%E a(5)-a(7) from _Andrew Howroyd_, Aug 10 2019
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