A326364 - OEIS

%I #10 Aug 12 2019 23:07:30

%S 1,0,0,2,426,987404,887044205940,291072121051815578010398,

%T 14704019422368226413234332571239460300433492086,

%U 12553242487939461785560846872353486129110194397301168776798213375239447299205732561174066488

%N Number of intersecting set systems with empty intersection (meaning there is no vertex in common to all the edges) covering n vertices.

%C Covering means there are no isolated vertices. A set system (set of sets) is intersecting if no two edges are disjoint.

%F Inverse binomial transform of A326373. - _Andrew Howroyd_, Aug 12 2019

%e The a(3) = 2 intersecting set systems with empty intersection:

%e   {{1,2},{1,3},{2,3}}

%e   {{1,2},{1,3},{2,3},{1,2,3}}

%t stableSets[u_,Q_]:=If[Length[u]==0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r==w||Q[r,w]||Q[w,r]],Q]]]];

%t Table[Length[Select[stableSets[Subsets[Range[n],{1,n}],Intersection[#1,#2]=={}&],And[Union@@#==Range[n],#=={}||Intersection@@#=={}]&]],{n,0,4}]

%Y Covering set systems with empty intersection are A318128.

%Y Covering, intersecting set systems are A305843.

%Y Covering, intersecting antichains with empty intersection are A326365.

%Y Cf. A006126, A007363, A014466, A051185, A058891, A305844, A307249, A318129, A326361, A326362, A326363.

%K nonn

%O 0,4

%A _Gus Wiseman_, Jul 01 2019

%E a(6)-a(9) from _Andrew Howroyd_, Aug 12 2019