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A327426
Number of non-connected, unlabeled, antichain covers of {1..n} (vertex-connectivity 0).
8
1, 1, 1, 2, 6, 23, 201, 16345
OFFSET
0,4
COMMENTS
An antichain is a set of sets, none of which is a subset of any other. It is covering if there are no isolated vertices. A singleton is not considered connected.
The vertex-connectivity of a set-system is the minimum number of vertices that must be removed (along with any resulting empty edges) to obtain a non-connected set-system or singleton. Note that this means a single node has vertex-connectivity 0.
FORMULA
a(n > 1) = A261005(n) - A261006(n).
EXAMPLE
Non-isomorphic representatives of the a(2) = 1 through a(5) = 23 antichains:
{1}{2} {1}{23} {1}{234} {1}{2345}
{1}{2}{3} {12}{34} {12}{345}
{1}{2}{34} {1}{2}{345}
{1}{24}{34} {1}{23}{45}
{1}{2}{3}{4} {12}{35}{45}
{1}{23}{24}{34} {1}{25}{345}
{1}{2}{3}{45}
{1}{245}{345}
{1}{2}{35}{45}
{1}{2}{3}{4}{5}
{1}{24}{35}{45}
{1}{25}{35}{45}
{12}{34}{35}{45}
{1}{24}{25}{345}
{1}{23}{245}{345}
{1}{2}{34}{35}{45}
{1}{235}{245}{345}
{1}{23}{24}{35}{45}
{1}{25}{34}{35}{45}
{1}{23}{24}{25}{345}
{1}{234}{235}{245}{345}
{1}{24}{25}{34}{35}{45}
{1}{23}{24}{25}{34}{35}{45}
CROSSREFS
Column k = 0 of A327359.
The labeled version is A120338.
The non-covering version is A327424 (partial sums).
Sequence in context: A358609 A364791 A020122 * A086554 A213324 A007672
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 11 2019
STATUS
approved