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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). 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

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.

REFERENCES

G. Kilibarda and V. Jovovic, "Enumeration of some classes of T_0-hypergraphs", in preparation, 2004.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Eric Weisstein's World of Mathematics, Minimal Cover.

FORMULA

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!.

EXAMPLE

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;

...

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A185664 A300812 A144209 * A062734 A205531 A269246

Adjacent sequences:  A094541 A094542 A094543 * A094545 A094546 A094547

KEYWORD

easy,nonn,tabl

AUTHOR

Goran Kilibarda, Vladeta Jovovic, May 08 2004

STATUS

approved

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Last modified October 17 21:57 EDT 2019. Contains 328134 sequences. (Running on oeis4.)