cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A094546 Number of n-member minimal T_0-covers.

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%I A094546 #15 Feb 16 2025 08:32:53
%S A094546 1,1,4,1457,112632827396,158158632767281777075441633086607,
%T A094546 6800377846899806825426438402771408584453689087636553015800284773113817943589005365456
%N A094546 Number of n-member minimal T_0-covers.
%C A094546 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 A094546 G. C. Greubel, <a href="/A094546/b094546.txt">Table of n, a(n) for n = 0..8</a>
%H A094546 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 A094546 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalCover.html">Minimal Cover</a>.
%F A094546 a(n) = Sum_{m=n..2^n-1} m!/n!*binomial(2^n-n-1, m-n).
%t A094546 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 *)
%o A094546 (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
%Y A094546 Cf. A035348, A046165, A094545.
%Y A094546 Column sums of A094544.
%K A094546 easy,nonn
%O A094546 0,3
%A A094546 Goran Kilibarda and _Vladeta Jovovic_, May 08 2004