OFFSET
1,2
COMMENTS
For k=1, these numbers are the Dedekind numbers A007153 counting the number of monotone Boolean functions or antichains of subsets of an n-set containing at least one nonempty set.
For k=2, these numbers are Antichain-Boolean numbers, see A374821.
These numbers are given by a polynomial in k for fixed n when k>=n.
LINKS
Sara Billey and Matjaž Konvalinka, Generalized rank functions and quilts of alternating sign matrices, arXiv:2412.03236 [math.CO], 2024. See p. 32.
EXAMPLE
Square array begins:
1, 2, 3, 4, 5, 6, ...
4, 4, 17, 46, 100, ...
18, 199, 199, 3252, ...
166, 47000, 3813042, ...
7579, 410131245, ...
7828352, ...
CROSSREFS
KEYWORD
AUTHOR
Sara Billey and Matjaz Konvalinka, Jul 21 2024
STATUS
approved