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Number of unlabeled set-systems (without {}) on n vertices that are closed under intersection.
5

%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