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 A058711 #38 Oct 10 2019 04:28:14
%S A058711 1,1,1,1,4,1,1,14,11,1,1,51,106,26,1,1,202,1232,642,57,1,1,876,22172,
%T A058711 28367,3592,120,1,1,4139,803583,8274374,991829,19903,247,1
%N A058711 Triangle T(n,k) giving the number of loopless matroids of rank k on n labeled points (n >= 1, 1 <= k <= n).
%C A058711 From _Petros Hadjicostas_, Oct 09 2019: (Start)
%C A058711 The old references had some typos, some of which were corrected in the recent ones. Few additional typos were corrected here from the recent references. Here are some of the changes: T(5,2) = 31 --> 51; T(5,4) = 21 --> 26; sum of row n=5 is 185 (not 160 or 165); T(8,3) = 686515 --> 803583; T(8, 6) = 19904 --> 19903, and some others.
%C A058711 This triangular array is the same as A058710 except that it has no row n = 0 and no column k = 0.
%C A058711 (End)
%H A058711 W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/matroid.html">Tables of matroids</a>.
%H A058711 W. M. B. Dukes, <a href="https://web.archive.org/web/20030208144026/http://www.stp.dias.ie/~dukes/phd.html">Counting and Probability in Matroid Theory</a>, Ph.D. Thesis, Trinity College, Dublin, 2000.
%H A058711 W. M. B. Dukes, <a href="https://arxiv.org/abs/math/0411557">The number of matroids on a finite set</a>, arXiv:math/0411557 [math.CO], 2004.
%H A058711 W. M. B. Dukes, <a href="http://emis.impa.br/EMIS/journals/SLC/wpapers/s51dukes.html">On the number of matroids on a finite set</a>, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g.
%H A058711 <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%F A058711 From _Petros Hadjicostas_, Oct 09 2019: (Start)
%F A058711 T(n,1) = 1 for n >= 1.
%F A058711 T(n,2) = Bell(n) - 1 = A000110(n) - 1 = A058692(n) for n >= 2.
%F A058711 T(n,3) = Sum_{i = 3..n} Stirling2(n,i) * (A056642(i) - 1) = Sum_{i = 3..n} A008277(n,i) * A058720(i,3) for n >= 3.
%F A058711 T(n,k) = Sum_{i = k..n} Stirling2(n,i) * A058720(i,k) for n >= k. [Dukes (2004), p. 3; see the equation with the Stirling numbers of the second kind.]
%F A058711 (End)
%e A058711 Table T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
%e A058711 1;
%e A058711 1, 1;
%e A058711 1, 4, 1;
%e A058711 1, 14, 11, 1;
%e A058711 1, 51, 106, 26, 1;
%e A058711 1, 202, 1232, 642, 57, 1;
%e A058711 1, 876, 22172, 28367, 3592, 120, 1;
%e A058711 1, 4139, 803583, 8274374, 991829, 19903, 247, 1;
%e A058711 ...
%Y A058711 Same as A058710 (except for row n=0 and column k=0).
%Y A058711 Row sums give A058712.
%Y A058711 Columns include (truncated versions of) A000012 (k=1), A058692 (k=2), A058715 (k=3).
%K A058711 nonn,nice,tabl,more
%O A058711 1,5
%A A058711 _N. J. A. Sloane_, Dec 31 2000
%E A058711 Several values corrected by _Petros Hadjicostas_, Oct 09 2019