A094545 -id:A094545 - cp's OEIS frontend

A109995 Number of unlabeled ordered minimal T_0-covers of an n-set, cf. A094545.

1, 1, 1, 2, 5, 18, 86, 549, 4647, 52060, 772976, 15240116, 400345371, 14063594530, 663256392496, 42161077371566, 3625838175218123, 423372648479289300, 67333725775723184308, 14628921614102655999804, 4352732830667872529962044

Offset: 0

Goran Kilibarda, Vladeta Jovovic, Sep 01 2005

G. C. Greubel, Table of n, a(n) for n = 0..119

Table[Sum[Binomial[2^m-m-1, n-m], {m,0,n}], {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)

for(n=0,50, print1(sum(m=0,n, binomial(2^m -m -1, n-m)), ", ")) \\ G. C. Greubel, Oct 08 2017

a(n) = Sum_{m=0..n} binomial(2^m-m-1, n-m).

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

Original entry on oeis.org

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!.

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

A109995 Number of unlabeled ordered minimal T_0-covers of an n-set, cf. A094545.

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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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A094546 Number of n-member minimal T_0-covers.

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