OFFSET
0,9
COMMENTS
A cover of a set is a T_0-cover if for every two distinct points of the set there exists a member (block) of the cover containing one but not the other point.
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
Eric Weisstein's World of Mathematics, Minimal Cover.
FORMULA
a(n, m) = n!/m!*binomial(2^m-m-1, n-m).
E.g.f.: Sum_{n>=0} y^n*(1+y)^(2^n-n-1)*x^n/n!.
EXAMPLE
1;
0, 1;
0, 0, 1;
0, 0, 3, 1;
0, 0, 0, 16, 1;
0, 0, 0, 120, 55, 1;
0, 0, 0, 480, 1650, 156, 1;
...
MATHEMATICA
Flatten[Table[n!/m! Binomial[2^m-m-1, n-m], {n, 0, 10}, {m, 0, n}]] (* Harvey P. Dale, Jan 16 2012 *)
CROSSREFS
KEYWORD
AUTHOR
Goran Kilibarda and Vladeta Jovovic, May 08 2004
STATUS
approved