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Number of minimal T_0-covers of an n-set.
3

%I #13 Aug 28 2024 00:48:23

%S 1,1,1,4,17,176,2287,49540,1518337,67457584,4254836111,376795261844,

%T 46709151254449,8061849904932136,1936383997541071639,

%U 646603398091877815516,300476951799493029958913

%N Number of minimal T_0-covers of an n-set.

%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.

%C Row sums of A094544.

%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) = Sum_{m=0..n} (n!/m!)*binomial(2^m-m-1, n-m).

%F a(n) = Sum_{m=0..n} Stirling1(n, m)*A046165(m).

%F E.g.f.: Sum_{n>=0} x^n*(1+x)^(2^n-n-1)/n!.

%Y Cf. A035348, A046165, A094544, A094546.

%K easy,nonn

%O 0,4

%A Goran Kilibarda and _Vladeta Jovovic_, May 08 2004