|
%I #16 Dec 17 2022 12:49:07
%S 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,
%T 0,0,840,34650,13650,399,1,0,0,0,0,554400,873600,89376,960,1,0,0,0,0,
%U 6985440,45208800,14747040,514080,2223,1,0,0,0,0,69854400,1989187200
%N Triangle of a(n,m) = number of m-member minimal T_0-covers of an n-set (n >= 0, 0<= m <=n).
%C 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.
%H G. C. Greubel, <a href="/A094544/b094544.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%H Goran Kilibarda and Vladeta Jovovic, <a href="https://arxiv.org/abs/1411.4187">Enumeration of some classes of T_0-hypergraphs</a>, arXiv:1411.4187 [math.CO], 2014.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalCover.html">Minimal Cover</a>.
%F a(n, m) = n!/m!*binomial(2^m-m-1, n-m).
%F E.g.f.: Sum_{n>=0} y^n*(1+y)^(2^n-n-1)*x^n/n!.
%e 1;
%e 0, 1;
%e 0, 0, 1;
%e 0, 0, 3, 1;
%e 0, 0, 0, 16, 1;
%e 0, 0, 0, 120, 55, 1;
%e 0, 0, 0, 480, 1650, 156, 1;
%e ...
%t Flatten[Table[n!/m! Binomial[2^m-m-1,n-m],{n,0,10},{m,0,n}]] (* _Harvey P. Dale_, Jan 16 2012 *)
%Y Cf. A035348, A046165, A094545 (row sums), A094546 (column sums).
%K easy,nonn,tabl
%O 0,9
%A Goran Kilibarda and _Vladeta Jovovic_, May 08 2004
|
