A094546 -id:A094546 - cp's OEIS frontend

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

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.

			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;
...

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.

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

Flatten[Table[n!/m! Binomial[2^m-m-1,n-m],{n,0,10},{m,0,n}]] (* Harvey P. Dale, Jan 16 2012 *)

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!.

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

Original entry on oeis.org

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!.

cp's OEIS Frontend

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

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