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 A331277 #12 Jan 23 2020 16:45:33
%S A331277 1,1,1,0,1,1,0,1,1,1,0,1,6,1,1,0,1,62,31,1,1,0,1,900,2649,160,1,1,0,1,
%T A331277 16824,441061,116360,841,1,1,0,1,384668,121105865,231173330,5364701,
%U A331277 4494,1,1,0,1,10398480,49615422851,974787170226,131147294251,256452714,24319,1,1
%N A331277 Array read by antidiagonals: A(n,k) is the number of binary matrices with k distinct columns and any number of nonzero rows with n ones in every column and columns in decreasing lexicographic order.
%C A331277 The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.
%C A331277 A(n,k) is the number of labeled n-uniform hypergraphs with k edges and no isolated vertices. When n=2 these objects are graphs.
%H A331277 Andrew Howroyd, <a href="/A331277/b331277.txt">Table of n, a(n) for n = 0..1325</a>
%F A331277 A(n, k) = Sum_{j=0..n*k} binomial(binomial(j,n),k) * (Sum_{i=j..n*k} (-1)^(i-j)*binomial(i,j)).
%F A331277 A(n, k) = Sum_{j=0..k} Stirling1(k, j)*A262809(n, j)/k!.
%F A331277 A(n, k) = Sum_{j=0..k} (-1)^(k-j)*binomial(k-1, k-j)*A330942(n, j).
%F A331277 A331639(n) = Sum_{d|n} A(n/d, d).
%e A331277 Array begins:
%e A331277 ====================================================================
%e A331277 n\k | 0 1 2 3 4 5 6
%e A331277 ----+---------------------------------------------------------------
%e A331277 0 | 1 1 0 0 0 0 0 ...
%e A331277 1 | 1 1 1 1 1 1 1 ...
%e A331277 2 | 1 1 6 62 900 16824 384668 ...
%e A331277 3 | 1 1 31 2649 441061 121105865 49615422851 ...
%e A331277 4 | 1 1 160 116360 231173330 974787170226 ...
%e A331277 5 | 1 1 841 5364701 131147294251 ...
%e A331277 6 | 1 1 4494 256452714 78649359753286 ...
%e A331277 ...
%e A331277 The A(2,2) = 6 matrices are:
%e A331277 [1 0] [1 0] [1 0] [1 1] [1 0] [1 0]
%e A331277 [1 0] [0 1] [0 1] [1 0] [1 1] [0 1]
%e A331277 [0 1] [1 0] [0 1] [0 1] [0 1] [1 1]
%e A331277 [0 1] [0 1] [1 0]
%o A331277 (PARI) T(n,k)={my(m=n*k); sum(j=0, m, binomial(binomial(j,n), k)*sum(i=j, m, (-1)^(i-j)*binomial(i, j)))}
%Y A331277 Rows n=1..3 are A000012, A121251, A136245.
%Y A331277 Columns k=0..3 are A000012, A000012, A047665, A137219.
%Y A331277 The version with nonnegative integer entries is A331278.
%Y A331277 The version with not necessarily distinct columns is A330942.
%Y A331277 Cf. A262809 (unrestricted version), A331315, A331639.
%K A331277 nonn,tabl
%O A331277 0,13
%A A331277 _Andrew Howroyd_, Jan 13 2020