A094544 Triangle of a(n,m) = number of m-member minimal T_0-covers of an n-set (n >= 0, 0<= m <=n).

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

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

Cf. A035348, A046165, A094545 (row sums), A094546 (column sums).

Sequence in context: A185664 A300812 A144209 * A062734 A336567 A361902

Adjacent sequences: A094541 A094542 A094543 * A094545 A094546 A094547

Keyword

easy,nonn,tabl

Author

Goran Kilibarda and Vladeta Jovovic, May 08 2004

Status

approved