A330124 - OEIS

%I #7 Dec 06 2019 09:36:30

%S 1,1,2,22,1776

%N Number of unlabeled set-systems with n vertices and 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) = 22 set-systems:

%e   0

%e   {1}{2}{12}

%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 Partial sums of the covering case A330196.

%Y The labeled version is A330059.

%Y The "multi" version is A302545.

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

%Y Unlabeled set-systems with no singletons are A317794.

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

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

%Y The case with no singletons is A320665.

%Y Cf. A007716, A016031, A306005, A317795, A321405, A330052, A330055.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Dec 05 2019