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.
%I A055080 #28 Feb 16 2025 08:32:42
%S A055080 1,1,1,1,2,1,1,4,3,1,1,6,9,4,1,1,9,23,17,5,1,1,12,51,65,28,6,1,1,16,
%T A055080 103,230,156,43,7,1,1,20,196,736,863,336,62,8,1,1,25,348,2197,4571,
%U A055080 2864,664,86,9,1,1,30,590,6093,22952,25326,8609,1229,115,10,1,1,36,960
%N A055080 Triangle T(n,k) read by rows, giving number of k-member minimal covers of an unlabeled n-set, k=1..n.
%C A055080 Also number of unlabeled split graphs on n vertices and with a k-element clique (cf. A048194).
%H A055080 Andrew Howroyd, <a href="/A055080/b055080.txt">Table of n, a(n) for n = 1..1275</a> (first 50 rows)
%H A055080 R. J. Clarke, <a href="http://dx.doi.org/10.1016/0012-365X(90)90146-9">Covering a set by subsets</a>, Discrete Math., 81 (1990), 147-152.
%H A055080 Vladeta Jovovic, <a href="/A005748/a005748.pdf">Binary matrices up to row and column permutations</a>
%H A055080 G. F. Royle, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/ROYLE/royle.html">Counting Set Covers and Split Graphs</a>, J. Integer Seqs., 3 (2000), #00.2.6.
%H A055080 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalCover.html">Minimal covers</a>
%F A055080 T(n,k) = A028657(n,k) - A028657(n-1,k). - _Andrew Howroyd_, Feb 28 2023
%e A055080 Triangle begins:
%e A055080 1;
%e A055080 1, 1;
%e A055080 1, 2, 1;
%e A055080 1, 4, 3, 1;
%e A055080 1, 6, 9, 4, 1;
%e A055080 1, 9, 23, 17, 5, 1;
%e A055080 1, 12, 51, 65, 28, 6, 1;
%e A055080 1, 16, 103, 230, 156, 43, 7, 1;
%e A055080 1, 20, 196, 736, 863, 336, 62, 8, 1;
%e A055080 ...
%e A055080 There are four minimal covers of an unlabeled 3-set: one 1-cover {{1,2,3}}, two 2-covers {{1,2},{3}}, {{1,2},{1,3}} and one 3-cover {{1},{2},{3}}.
%o A055080 (PARI) \\ Needs A(n,m) from A028657.
%o A055080 T(n,k) = A(n-k, k) - if(k<n, A(n-1-k, k))
%o A055080 { for(n=1, 10, for(k=1, n, print1(T(n,k), ", ")); print) } \\ _Andrew Howroyd_, Feb 28 2023
%Y A055080 Row sums give A048194.
%Y A055080 Columns are A000012, A087811, A005783, A005784, A005785 A005786, A055066.
%Y A055080 Diagonals are A000012, A000027, A005744, A005745, A005746, A005771, A005747, A005748.
%Y A055080 Cf. A035348 for labeled case.
%Y A055080 Cf. A002620, A028657.
%K A055080 nonn,tabl
%O A055080 1,5
%A A055080 _Vladeta Jovovic_, Jun 13 2000