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 A347699 #7 Oct 14 2021 18:05:37 %S A347699 1,1,1,1,1,2,1,1,4,3,1,1,6,9,4,1,1,9,23,17,5 %N A347699 Triangle read by rows: For n >= 1, 0 <= k <= n-1, T(n,k) = 0 if k=0, otherwise the number of inequivalent k X (n-k) 0,1 matrices having at least one 1 in each column. %C A347699 It appears that this is essentially the same as the triangle in A055080, except that the 1's at the ends of the rows in A055080 have been moved to the start of the rows. (This is at present only a conjecture.) %C A347699 Even if the conjecture turns out to be true, this triangle deserves its own entry because the arrays look so different. %C A347699 The conjecture would imply the row sums are given by A048194. %H A347699 H. Sharp, Jr., <a href="https://doi.org/10.1016/0012-365X(73)90081-2">Enumeration of vacuously transitive relations</a>, Discrete Math. 4 (1973), 185-196. %e A347699 Triangle begins: %e A347699 1; %e A347699 1, 1; %e A347699 1, 1, 2; %e A347699 1, 1, 4, 3; %e A347699 1, 1, 6, 9, 4; %e A347699 1, 1, 9, 23, 17, 5; %e A347699 ... %Y A347699 Cf. A048194, A055080, A347700. %K A347699 nonn,tabl,more %O A347699 1,6 %A A347699 _N. J. A. Sloane_, Oct 13 2021