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 A331509 #10 Feb 20 2022 11:32:39 %S A331509 1,1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,3,0,0,1,0,1,6,3,0,0,1,0,1,15,19,1, %T A331509 0,0,1,0,1,42,141,29,0,0,0,1,0,1,109,1571,769,23,0,0,0,1,0,1,320 %N A331509 Array read by antidiagonals: A(n,k) is the number of nonisomorphic T_0 n-regular set-systems on a k-set. %C A331509 An n-regular set-system is a finite set of nonempty sets in which each element appears in n blocks. %C A331509 A set-system is T_0 if for every two distinct elements there exists a block containing one but not the other element. %C A331509 A(n,k) is the number of nonequivalent binary matrices with k distinct columns and any number of distinct nonzero rows with n ones in every column up to permutation of rows and columns. %e A331509 Array begins: %e A331509 ================================= %e A331509 n\k | 0 1 2 3 4 5 6 7 %e A331509 ----+---------------------------- %e A331509 0 | 1 1 0 0 0 0 0 0 ... %e A331509 1 | 1 1 1 1 1 1 1 1 ... %e A331509 2 | 1 0 1 3 6 15 42 109 ... %e A331509 3 | 1 0 0 3 19 141 1571 ... %e A331509 4 | 1 0 0 1 29 769 ... %e A331509 5 | 1 0 0 0 23 ... %e A331509 ... %e A331509 The A(2,3) = 3 matrices are: %e A331509 [1 1 1] [1 1 0] [1 1 0] %e A331509 [1 0 0] [1 0 1] [1 0 1] %e A331509 [0 1 0] [0 1 0] [0 1 1] %e A331509 [0 0 1] [0 0 1] %Y A331509 Row 2 appears to be A005368. Row 3 is A331716. %Y A331509 Cf. A330942, A331039, A331461, A331508, A331510. %K A331509 nonn,tabl,more %O A331509 0,18 %A A331509 _Andrew Howroyd_, Jan 18 2020