

A326881


Number of setsystems with {} that are closed under intersection and cover n vertices.


13




OFFSET

0,3


LINKS

Table of n, a(n) for n=0..7.


FORMULA

Inverse binomial transform of A102895.  Andrew Howroyd, Aug 10 2019


EXAMPLE

The a(2) = 5 setsystems:
{{},{1,2}}
{{},{1},{2}}
{{},{1},{1,2}}
{{},{2},{1,2}}
{{},{1},{2},{1,2}}


MATHEMATICA

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


CROSSREFS

The case also closed under union is A000798.
The connected case (i.e., with maximum) is A102894.
The same for union instead of intersection is (also) A102894.
The noncovering case is A102895.
The BIInumbers of these setsystems (without the empty set) are A326880.
The unlabeled case is A326883.
Cf. A003465, A014466, A102896, A102897, A193674, A193675, A306445, A307249, A326878.
Sequence in context: A193436 A193501 A133990 * A120808 A092204 A079874
Adjacent sequences: A326878 A326879 A326880 * A326882 A326883 A326884


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jul 30 2019


EXTENSIONS

a(5)a(7) from Andrew Howroyd, Aug 10 2019


STATUS

approved



