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A094544
Triangle of a(n,m) = number of m-member minimal T_0-covers of an n-set (n >= 0, 0<= m <=n).
3
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, 0, 0, 0, 840, 34650, 13650, 399, 1, 0, 0, 0, 0, 554400, 873600, 89376, 960, 1, 0, 0, 0, 0, 6985440, 45208800, 14747040, 514080, 2223, 1, 0, 0, 0, 0, 69854400, 1989187200
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
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
Cf. A035348, A046165, A094545 (row sums), A094546 (column sums).
Sequence in context: A300812 A373417 A144209 * A062734 A336567 A361902
KEYWORD
easy,nonn,tabl
AUTHOR
Goran Kilibarda and Vladeta Jovovic, May 08 2004
STATUS
approved