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Number of unlabeled set-systems covering n vertices with no endpoints.
1

%I #5 Dec 06 2019 09:36:37

%S 1,0,1,20,1754

%N Number of unlabeled set-systems covering n vertices with no endpoints.

%C A set-system is a finite set of finite nonempty sets. An endpoint is a vertex appearing only once (degree 1).

%e Non-isomorphic representatives of the a(3) = 20 set-systems:

%e {12}{13}{23}

%e {1}{23}{123}

%e {12}{13}{123}

%e {1}{2}{13}{23}

%e {1}{2}{3}{123}

%e {1}{12}{13}{23}

%e {1}{2}{13}{123}

%e {1}{12}{13}{123}

%e {1}{12}{23}{123}

%e {12}{13}{23}{123}

%e {1}{2}{3}{12}{13}

%e {1}{2}{12}{13}{23}

%e {1}{2}{3}{12}{123}

%e {1}{2}{12}{13}{123}

%e {1}{2}{13}{23}{123}

%e {1}{12}{13}{23}{123}

%e {1}{2}{3}{12}{13}{23}

%e {1}{2}{3}{12}{13}{123}

%e {1}{2}{12}{13}{23}{123}

%e {1}{2}{3}{12}{13}{23}{123}

%Y First differences of the non-covering version A330124.

%Y The "multi" version is A302545.

%Y Unlabeled set-systems with no endpoints counted by vertices are A317794.

%Y Unlabeled set-systems with no endpoints counted by weight are A330054.

%Y Unlabeled set-systems counted by vertices are A000612.

%Y Unlabeled set-systems counted by weight are A283877.

%Y Cf. A007716, A016031, A306005, A317795, A320665, A330052, A330053, A330055.

%K nonn,more

%O 0,4

%A _Gus Wiseman_, Dec 05 2019