A094546 - OEIS

%I #15 Feb 16 2025 08:32:53

%S 1,1,4,1457,112632827396,158158632767281777075441633086607,

%T 6800377846899806825426438402771408584453689087636553015800284773113817943589005365456

%N Number of n-member minimal T_0-covers.

%C 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.

%H G. C. Greubel, <a href="/A094546/b094546.txt">Table of n, a(n) for n = 0..8</a>

%H Goran Kilibarda and Vladeta Jovovic, <a href="https://arxiv.org/abs/1411.4187">Enumeration of some classes of T_0-hypergraphs</a>, arXiv:1411.4187 [math.CO], 2014.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalCover.html">Minimal Cover</a>.

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

%t 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 *)

%o (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

%Y Cf. A035348, A046165, A094545.

%Y Column sums of A094544.

%K easy,nonn

%O 0,3

%A Goran Kilibarda and _Vladeta Jovovic_, May 08 2004