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 A057150 #21 Sep 10 2019 09:11:41
%S A057150 1,0,1,0,1,1,0,1,2,1,0,0,5,2,1,0,0,4,11,2,1,0,0,3,21,14,2,1,0,0,1,34,
%T A057150 49,15,2,1,0,0,1,33,131,69,15,2,1,0,0,0,33,248,288,79,15,2,1,0,0,0,19,
%U A057150 410,840,420,82,15,2,1,0,0,0,14,531,2144,1744,497,83,15,2,1
%N A057150 Triangle read by rows: T(n,k) = number of k X k binary matrices with n ones, with no zero rows or columns, up to row and column permutation.
%C A057150 Also the number of non-isomorphic set multipartitions (multisets of sets) of weight n with k parts and k vertices. - _Gus Wiseman_, Nov 14 2018
%e A057150 [1], [0,1], [0,1,1], [0,1,2,1], [0,0,5,2,1], [0,0,4,11,2,1], ...;
%e A057150 There are 8 square binary matrices with 5 ones, with no zero rows or columns, up to row and column permutation: 5 of size 3 X 3:
%e A057150 [0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1]
%e A057150 [0 0 1] [0 1 0] [0 1 1] [0 1 1] [1 1 0]
%e A057150 [1 1 1] [1 1 1] [1 0 1] [1 1 0] [1 1 0]
%e A057150 2 of size 4 X 4:
%e A057150 [0 0 0 1] [0 0 0 1]
%e A057150 [0 0 0 1] [0 0 1 0]
%e A057150 [0 0 1 0] [0 1 0 0]
%e A057150 [1 1 0 0] [1 0 0 1]
%e A057150 and 1 of size 5 X 5:
%e A057150 [0 0 0 0 1]
%e A057150 [0 0 0 1 0]
%e A057150 [0 0 1 0 0]
%e A057150 [0 1 0 0 0]
%e A057150 [1 0 0 0 0].
%e A057150 From _Gus Wiseman_, Nov 14 2018: (Start)
%e A057150 Triangle begins:
%e A057150 1
%e A057150 0 1
%e A057150 0 1 1
%e A057150 0 1 2 1
%e A057150 0 0 5 2 1
%e A057150 0 0 4 11 2 1
%e A057150 0 0 3 21 14 2 1
%e A057150 0 0 1 34 49 15 2 1
%e A057150 0 0 1 33 131 69 15 2 1
%e A057150 0 0 0 33 248 288 79 15 2 1
%e A057150 Non-isomorphic representatives of the multiset partitions counted in row 6 {0,0,4,11,2,1} are:
%e A057150 {{12}{13}{23}} {{1}{1}{1}{234}} {{1}{2}{3}{3}{45}} {{1}{2}{3}{4}{5}{6}}
%e A057150 {{1}{23}{123}} {{1}{1}{24}{34}} {{1}{2}{3}{5}{45}}
%e A057150 {{13}{23}{23}} {{1}{1}{4}{234}}
%e A057150 {{3}{23}{123}} {{1}{2}{34}{34}}
%e A057150 {{1}{3}{24}{34}}
%e A057150 {{1}{3}{4}{234}}
%e A057150 {{1}{4}{24}{34}}
%e A057150 {{1}{4}{4}{234}}
%e A057150 {{2}{4}{12}{34}}
%e A057150 {{3}{4}{12}{34}}
%e A057150 {{4}{4}{12}{34}}
%e A057150 (End)
%t A057150 permcount[v_List] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
%t A057150 c[p_List, q_List, k_] := SeriesCoefficient[Product[Product[(1 + O[x]^(k + 1) + x^LCM[p[[i]], q[[j]]])^GCD[p[[i]], q[[j]]], {j, 1, Length[q]}], {i, 1, Length[p]}], {x, 0, k}];
%t A057150 M[m_, n_, k_] := M[m, n, k] = Module[{s = 0}, Do[Do[s += permcount[p]* permcount[q]*c[p, q, k], {q, IntegerPartitions[n]}], {p, IntegerPartitions[m]}]; s/(m!*n!)];
%t A057150 T[n_, k_] := M[k, k, n] - 2*M[k, k - 1, n] + M[k - 1, k - 1, n];
%t A057150 Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 10 2019, after _Andrew Howroyd_ *)
%o A057150 (PARI) \\ See A321609 for M.
%o A057150 T(n,k) = M(k,k,n) - 2*M(k,k-1,n) + M(k-1,k-1,n); \\ _Andrew Howroyd_, Nov 14 2018
%Y A057150 Row sums give A057151.
%Y A057150 Cf. A049311, A056037, A056079, A056080, A057149, A057151, A057152.
%Y A057150 Cf. A007716, A048291, A054976, A101370, A104601, A104602, A120732, A120733, A135588, A319616, A321609, A321615.
%K A057150 nonn,tabl
%O A057150 1,9
%A A057150 _Vladeta Jovovic_, Aug 14 2000
%E A057150 Duplicate seventh row removed by _Gus Wiseman_, Nov 14 2018