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 A053534 #45 Oct 11 2019 06:31:25
%S A053534 1,1,1,1,2,1,1,3,3,1,1,4,7,4,1,1,5,13,13,5,1,1,6,23,38,23,6,1,1,7,37,
%T A053534 108,108,37,7,1,1,8,58,325,940,325,58,8,1,1,9,87,1275,190214,190214,
%U A053534 1275,87,9,1
%N A053534 Triangle T(n,k) giving number of pairwise non-isomorphic (i.e., unlabeled) matroids of rank k on n points (n >= 0, 0 <= k <= n).
%H A053534 W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/matroid.html">Tables of matroids</a>.
%H A053534 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 A053534 W. M. B. Dukes, <a href="http://arXiv.org/abs/math.CO/0411557">The number of matroids on a finite set</a>, arXiv:math/0411557 [math.CO], 2004.
%H A053534 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 A053534 Dillon Mayhew and Gordon F. Royle, <a href="http://arXiv.org/abs/math.CO/0702316">Matroids with nine elements</a>, arXiv:math/0702316 [math.CO], 2007 (see p. 7).
%H A053534 Dillon Mayhew and Gordon F. Royle, <a href="https://doi.org/10.1016/j.jctb.2007.07.005">Matroids with nine elements</a>, J. Combin. Theory Ser. B 98(2) (2008), 415-431.
%H A053534 <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%F A053534 From _Petros Hadjicostas_, Oct 10 2019: (Start)
%F A053534 T(n,0) = 1 for n >= 0.
%F A053534 T(n,1) = n for n >= 1.
%F A053534 T(n,2) = -n + Sum_{k = 1..n} p(k) for n >= 2, where p(k) = A000041(k). [Dukes (2004), Theorem 2.1.] (End)
%e A053534 The triangle, transposed, begins:
%e A053534 k...n=0...n=1...n=2...n=3...n=4...n=5...n=6...n=7...n=8...n=9...
%e A053534 0.|.1.....1.....1.....1.....1.....1.....1.....1.....1.......1.....
%e A053534 1.|.......1.....2.....3.....4.....5.....6.....7.....8.......9.....
%e A053534 2.|.............1.....3.....7....13....23....37....58......87.....
%e A053534 3.|...................1.....4....13....38...108...325....1275.....
%e A053534 4.|.........................1.....5....23...108...940..190214.....
%e A053534 5.|...............................1.....6....37...325..190214.....
%e A053534 6.|.....................................1.....7....58....1275.....
%e A053534 7.|...........................................1.....8......87.....
%e A053534 8.|.................................................1.......9.....
%e A053534 9.|.........................................................1.....
%e A053534 Sum.1.....2.....4.....8....17....38....98...306..1724..383172
%Y A053534 Row sums give A055545.
%Y A053534 Columns include (truncated versions of) A000012 (k=0), A000027 (k=1), A058682 (k=2), A058693 (k=3).
%Y A053534 Cf. A000041, A058669.
%K A053534 nonn,tabl,nice
%O A053534 0,5
%A A053534 _N. J. A. Sloane_, Dec 30 2000
%E A053534 More terms from _Jonathan Vos Post_, Feb 14 2007
%E A053534 Edited by _N. J. A. Sloane_, Jul 03 2008 at the suggestion of _R. J. Mathar_ and _Max Alekseyev_