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A094546 Number of n-member minimal T_0-covers. 3
1, 1, 4, 1457, 112632827396, 158158632767281777075441633086607, 6800377846899806825426438402771408584453689087636553015800284773113817943589005365456 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 n = 0..8

Eric Weisstein's World of Mathematics, Minimal Cover.

FORMULA

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A035348, A046165, A094545.

Column sums of A094544.

Sequence in context: A030271 A301576 A160088 * A203035 A030253 A278549

Adjacent sequences:  A094543 A094544 A094545 * A094547 A094548 A094549

KEYWORD

easy,nonn,tabl

AUTHOR

Goran Kilibarda, Vladeta Jovovic, May 08 2004

STATUS

approved

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Last modified December 6 04:20 EST 2021. Contains 349562 sequences. (Running on oeis4.)