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 A331567 #16 Jan 25 2020 17:55:07
%S A331567 1,1,1,1,1,1,1,3,0,1,1,13,6,0,1,1,75,120,0,0,1,1,541,6174,1104,0,0,1,
%T A331567 1,4683,449520,413088,5040,0,0,1,1,47293,49686726,329520720,18481080,
%U A331567 0,0,0,1,1,545835,7455901320,491236986720,179438982360,522481680,0,0,0,1
%N A331567 Array read by antidiagonals: A(n,k) is the number of binary matrices with k columns and any number of distinct nonzero rows with n ones in every column.
%H A331567 Andrew Howroyd, <a href="/A331567/b331567.txt">Table of n, a(n) for n = 0..209</a>
%F A331567 A(n,k) = 0 for k > 0, n > 2^(k-1).
%F A331567 A(2^(k-1), k) = (2^k-1)! for k > 0.
%F A331567 A331643(n) = Sum_{d|n} A(n/d, d).
%e A331567 Array begins:
%e A331567 ===============================================================
%e A331567 n\k | 0 1 2 3 4 5 6
%e A331567 ----+----------------------------------------------------------
%e A331567 0 | 1 1 1 1 1 1 1 ...
%e A331567 1 | 1 1 3 13 75 541 4683 ...
%e A331567 2 | 1 0 6 120 6174 449520 49686726 ...
%e A331567 3 | 1 0 0 1104 413088 329520720 491236986720 ...
%e A331567 4 | 1 0 0 5040 18481080 179438982360 3785623968170400 ...
%e A331567 5 | 1 0 0 0 522481680 70302503250720 ...
%e A331567 6 | 1 0 0 0 7875584640 ...
%e A331567 ...
%e A331567 The A(2,2) = 6 matrices are:
%e A331567 [1 1] [1 1] [1 0] [1 0] [0 1] [0 1]
%e A331567 [1 0] [0 1] [1 1] [0 1] [1 1] [1 0]
%e A331567 [0 1] [1 0] [0 1] [1 1] [1 0] [1 1]
%o A331567 (PARI)
%o A331567 WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
%o A331567 D(p, n, k)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); WeighT(v)[n]^k/prod(i=1, #v, i^v[i]*v[i]!)}
%o A331567 T(n, k)={ my(m=n*k+1, q=Vec(exp(intformal(O(x^m) - x^n/(1-x)))), f=Vec(serlaplace(1/(1+x) + O(x*x^m))/(x-1))); if(n==0, 1, sum(j=1, m, my(s=0); forpart(p=j, s+=(-1)^#p*D(p, n, k), [1, n]); s*sum(i=j, m, q[i-j+1]*f[i]))); }
%Y A331567 Rows n=1..3 are A000670, A331640, A331641.
%Y A331567 Column k=5 is A331642.
%Y A331567 Cf. A188445, A330942, A331568, A331569, A331571, A331643.
%K A331567 nonn,tabl
%O A331567 0,8
%A A331567 _Andrew Howroyd_, Jan 20 2020