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 A331568 #11 Jan 25 2020 17:55:19
%S A331568 1,1,1,1,1,1,1,3,1,1,1,13,13,3,1,1,75,313,87,3,1,1,541,14797,11655,
%T A331568 539,5,1,1,4683,1095601,4498191,439779,2483,11,1,1,47293,119621653,
%U A331568 3611504823,1390686419,14699033,14567,13,1,1,545835,17943752233,5192498314767,12006713338683,397293740555,453027131,81669,19,1
%N A331568 Array read by antidiagonals: A(n,k) is the number of nonnegative integer matrices with k columns and any number of distinct nonzero rows with column sums n.
%H A331568 Andrew Howroyd, <a href="/A331568/b331568.txt">Table of n, a(n) for n = 0..209</a>
%F A331568 A331648(n) = Sum_{d|n} A(n/d, d).
%e A331568 Array begins:
%e A331568 ================================================================
%e A331568 n\k | 0 1 2 3 4 5
%e A331568 ----+-----------------------------------------------------------
%e A331568 0 | 1 1 1 1 1 1 ...
%e A331568 1 | 1 1 3 13 75 541 ...
%e A331568 2 | 1 1 13 313 14797 1095601 ...
%e A331568 3 | 1 3 87 11655 4498191 3611504823 ...
%e A331568 4 | 1 3 539 439779 1390686419 12006713338683 ...
%e A331568 5 | 1 5 2483 14699033 397293740555 37366422896708825 ...
%e A331568 6 | 1 11 14567 453027131 105326151279287 ...
%e A331568 ...
%e A331568 The A(2,2) = 13 matrices are:
%e A331568 [1 1] [1 1] [1 0] [1 0] [0 1] [0 1]
%e A331568 [1 0] [0 1] [1 1] [0 1] [1 1] [1 0]
%e A331568 [0 1] [1 0] [0 1] [1 1] [1 0] [1 1]
%e A331568 .
%e A331568 [2 1] [2 0] [1 2] [1 0] [0 2] [0 1] [2 2]
%e A331568 [0 1] [0 2] [1 0] [1 2] [2 0] [2 1]
%o A331568 (PARI)
%o A331568 EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
%o A331568 D(p, n, k)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); EulerT(v)[n]^k/prod(i=1, #v, i^v[i]*v[i]!)}
%o A331568 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 A331568 Rows n=0..3 are A000012, A000670, A331644, A331645.
%Y A331568 Columns k=0..3 are A000012, A032020, A331646, A331647.
%Y A331568 Cf. A219585, A331315, A331567, A331570, A331572, A331648.
%K A331568 nonn,tabl
%O A331568 0,8
%A A331568 _Andrew Howroyd_, Jan 21 2020