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%I #10 Aug 09 2019 11:23:57
%S 1,2,4,10,38,368,29328,216591692,5592326399531792
%N Number of unlabeled set-systems (without {}) on n vertices that are closed under intersection.
%C A set-system is a finite set of finite nonempty sets, so no two edges of such a set-system can be disjoint.
%C Apart from the offset the same as A193675. - _R. J. Mathar_, Aug 09 2019
%F a(n > 0) = 2 * A193674(n - 1).
%e Non-isomorphic representatives of the a(0) = 1 through a(3) = 10 set-systems:
%e {} {} {} {}
%e {{1}} {{1}} {{1}}
%e {{1,2}} {{1,2}}
%e {{2},{1,2}} {{1,2,3}}
%e {{2},{1,2}}
%e {{3},{1,2,3}}
%e {{2,3},{1,2,3}}
%e {{3},{1,3},{2,3}}
%e {{3},{2,3},{1,2,3}}
%e {{3},{1,3},{2,3},{1,2,3}}
%Y The covering case is A108800(n - 1).
%Y The case with an edge containing all of the vertices is A193674(n - 1).
%Y The case with union instead of intersection is A193674.
%Y The labeled version is A326901.
%Y Cf. A000798, A001930, A006058, A102895, A102898, A326876, A326866, A326878, A326882, A326903, A326906.
%K nonn,more
%O 0,2
%A _Gus Wiseman_, Aug 04 2019
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