A094546 Number of n-member minimal T_0-covers.

1, 1, 4, 1457, 112632827396, 158158632767281777075441633086607, 6800377846899806825426438402771408584453689087636553015800284773113817943589005365456

Offset: 0

Author

Goran Kilibarda and Vladeta Jovovic, May 08 2004

Keywords

• easy
• nonn

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 n = 0..8
• 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.

Crossrefs

Cf. A035348, A046165, A094545.

Column sums of A094544.

Programs

Mathematica

Table[Sum[(m!/n!)*Binomial[2^n - n - 1, m - n], {m, n, 2^n - 1}], {n, 0, 5}] (* G. C. Greubel, Oct 07 2017 *)

PARI

for(n=0,5, print1(sum(m=n,2^n -1, (m!/n!)*binomial(2^n-n-1, m-n)), ", ")) \\ G. C. Greubel, Oct 07 2017

Formula

a(n) = Sum_{m=n..2^n-1} m!/n!*binomial(2^n-n-1, m-n).