A326906 - OEIS

%I #4 Aug 03 2019 14:18:04

%S 2,2,8,90,4542,2747402,151930948472,28175295407840207894

%N Number of sets of subsets of {1..n} that are closed under union and cover all n vertices.

%C Differs from A102895 in having a(0) = 2 instead of 1.

%F a(n) = 2 * A102894(n).

%e The a(0) = 2 through a(2) = 8 sets of subsets:

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

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

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

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

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

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

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

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

%t Table[Length[Select[Subsets[Subsets[Range[n]]],Union@@#==Range[n]&&SubsetQ[#,Union@@@Tuples[#,2]]&]],{n,0,3}]

%Y The case without empty sets is A102894.

%Y The case with a single covering edge is A102895.

%Y Binomial transform is A102897.

%Y The case also closed under intersection is A326878 for n > 0.

%Y The same for intersection instead of union is (also) A326906.

%Y The unlabeled version is A326907.

%Y Cf. A000798, A102896, A102897, A108800, A193675, A306445, A326880, A326881, A326883.

%K nonn,more

%O 0,1

%A _Gus Wiseman_, Aug 03 2019