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Number of unlabeled antichains of nonempty sets covering n vertices where every two vertices appear together in some edge (cointersecting).
2

%I #4 Sep 11 2019 20:22:28

%S 1,1,1,2,6,54

%N Number of unlabeled antichains of nonempty sets covering n vertices where every two vertices appear together in some edge (cointersecting).

%C An antichain is a set of sets, none of which is a subset of any other. It is covering if there are no isolated vertices.

%e Non-isomorphic representatives of the a(1) = 1 through a(4) = 6 antichains:

%e {1} {12} {123} {1234}

%e {12}{13}{23} {12}{134}{234}

%e {124}{134}{234}

%e {12}{13}{14}{234}

%e {123}{124}{134}{234}

%e {12}{13}{14}{23}{24}{34}

%Y The labeled version is A327020.

%Y Unlabeled covering antichains are A261005.

%Y The weighted version is A327060.

%Y Cf. A006126, A014466, A055621, A293606, A293993, A305844, A307249, A319639, A326704, A327057, A327058, A327358, A327359.

%K nonn,more

%O 0,4

%A _Gus Wiseman_, Sep 11 2019