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 A058710 #38 Oct 10 2019 15:09:36
%S A058710 1,0,1,0,1,1,0,1,4,1,0,1,14,11,1,0,1,51,106,26,1,0,1,202,1232,642,57,
%T A058710 1,0,1,876,22172,28367,3592,120,1,0,1,4139,803583,8274374,991829,
%U A058710 19903,247,1
%N A058710 Triangle T(n,k) giving number of loopless matroids of rank k on n labeled points (n >= 0, 0 <= k <= n).
%C A058710 From _Petros Hadjicostas_, Oct 10 2019: (Start)
%C A058710 The old references have some typos, some of which were corrected in the recent references (in 2004). Few additional typos were corrected here from the recent references. Here are some of the changes: T(5,2) = 31 --> 51 (see the comment by _Ralf Stephan_ below); 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 A058710 This triangular array is the same as A058711 except that the current one has row n = 0 and column k = 0.
%C A058710 (End)
%H A058710 W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/matroid.html">Tables of matroids</a>.
%H A058710 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 A058710 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 A058710 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.
%F A058710 From _Petros Hadjicostas_, Oct 10 2019: (Start)
%F A058710 T(n,0) = 0^n for n >= 0.
%F A058710 T(n,1) = 1 for n >= 1.
%F A058710 T(n,2) = Bell(n) - 1 = A000110(n) - 1 = A058692(n) for n >= 2.
%F A058710 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 A058710 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 A058710 (End)
%e A058710 Triangle T(n,k) (with rows n >= 0 and columns k >= 0) begins as follows:
%e A058710 1;
%e A058710 0, 1;
%e A058710 0, 1, 1;
%e A058710 0, 1, 4, 1;
%e A058710 0, 1, 14, 11, 1;
%e A058710 0, 1, 51, 106, 26, 1;
%e A058710 0, 1, 202, 1232, 642, 57, 1;
%e A058710 0, 1, 876, 22172, 28367, 3592, 120, 1;
%e A058710 0, 1, 4139, 803583, 8274374, 991829, 19903, 247, 1;
%e A058710 ...
%Y A058710 Cf. Same as A058711 (except for row n=0 and column k=0).
%Y A058710 Row sums give A058712.
%Y A058710 Columns include (truncated versions of) A000007 (k=0), A000012 (k=1), A058692 (k=2), A058715 (k=3).
%K A058710 nonn,tabl,nice
%O A058710 0,9
%A A058710 _N. J. A. Sloane_, Dec 31 2000
%E A058710 T(5,2) corrected from 31 to 51 by _Ralf Stephan_, Nov 29 2004