A094544 -id:A094544 - cp's OEIS frontend

A094545 Number of minimal T_0-covers of an n-set.

1, 1, 1, 4, 17, 176, 2287, 49540, 1518337, 67457584, 4254836111, 376795261844, 46709151254449, 8061849904932136, 1936383997541071639, 646603398091877815516, 300476951799493029958913

Offset: 0

Goran Kilibarda and Vladeta Jovovic, May 08 2004

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.

Row sums of A094544.

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.

Cf. A035348, A046165, A094544, A094546.

a(n) = Sum_{m=0..n} (n!/m!)*binomial(2^m-m-1, n-m).
a(n) = Sum_{m=0..n} Stirling1(n, m)*A046165(m).
E.g.f.: Sum_{n>=0} x^n*(1+x)^(2^n-n-1)/n!.

A094546 Number of n-member minimal T_0-covers.

Original entry on oeis.org

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

Offset: 0

Goran Kilibarda and Vladeta Jovovic, May 08 2004

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.

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.

Cf. A035348, A046165, A094545.

Column sums of A094544.

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 *)

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

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

cp's OEIS Frontend

A094545 Number of minimal T_0-covers of an n-set.

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