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A327807
Triangle read by rows where T(n,k) is the number of unlabeled antichains of sets with n vertices and vertex-connectivity >= k.
1
1, 2, 0, 4, 1, 0, 9, 3, 2, 0, 29, 14, 10, 6, 0, 209, 157, 128, 91, 54, 0
OFFSET
0,2
COMMENTS
An antichain is a set of sets, none of which is a subset of any other.
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.
EXAMPLE
Triangle begins:
1
2 0
4 1 0
9 3 2 0
29 14 10 6 0
209 157 128 91 54 0
CROSSREFS
Column k = 0 is A306505.
Column k = 1 is A261006 (clutters), if we assume A261006(0) = A261006(1) = 0.
Column k = 2 is A305028 (blobs), if we assume A305028(0) = A305028(2) = 0.
Except for the first column, same as A327358 (the covering case).
The labeled version is A327806.
Sequence in context: A056859 A272098 A291929 * A188448 A370412 A355917
KEYWORD
nonn,tabl,more
AUTHOR
Gus Wiseman, Sep 26 2019
STATUS
approved