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 A321733 #12 Dec 15 2024 04:35:37
%S A321733 1,1,2,8,40,246,1816,15630,153592,1696760,20816358,280807868,
%T A321733 4131117440,65823490088,1129256780408
%N A321733 Number of (0,1)-matrices with n ones, no zero rows or columns, and the same row sums as column sums.
%e A321733 The a(4) = 40 matrices:
%e A321733 [1 1]
%e A321733 [1 1]
%e A321733 .
%e A321733 [1 1 0][1 1 0][1 0 1][1 0 1][1 0 0]
%e A321733 [1 0 0][0 0 1][1 0 0][0 1 0][0 1 1]
%e A321733 [0 0 1][1 0 0][0 1 0][1 0 0][0 1 0]
%e A321733 .
%e A321733 [1 0 0][0 1 1][0 1 0][0 1 0][0 1 0]
%e A321733 [0 0 1][1 0 0][1 1 0][1 0 1][0 1 1]
%e A321733 [0 1 1][1 0 0][0 0 1][0 1 0][1 0 0]
%e A321733 .
%e A321733 [0 1 0][0 0 1][0 0 1][0 0 1][0 0 1]
%e A321733 [0 0 1][1 1 0][1 0 0][0 1 0][0 0 1]
%e A321733 [1 0 1][0 1 0][0 1 1][1 0 1][1 1 0]
%e A321733 .
%e A321733 [1 0 0 0][1 0 0 0][1 0 0 0][1 0 0 0][1 0 0 0][1 0 0 0]
%e A321733 [0 1 0 0][0 1 0 0][0 0 1 0][0 0 1 0][0 0 0 1][0 0 0 1]
%e A321733 [0 0 1 0][0 0 0 1][0 1 0 0][0 0 0 1][0 1 0 0][0 0 1 0]
%e A321733 [0 0 0 1][0 0 1 0][0 0 0 1][0 1 0 0][0 0 1 0][0 1 0 0]
%e A321733 .
%e A321733 [0 1 0 0][0 1 0 0][0 1 0 0][0 1 0 0][0 1 0 0][0 1 0 0]
%e A321733 [1 0 0 0][1 0 0 0][0 0 1 0][0 0 1 0][0 0 0 1][0 0 0 1]
%e A321733 [0 0 1 0][0 0 0 1][1 0 0 0][0 0 0 1][1 0 0 0][0 0 1 0]
%e A321733 [0 0 0 1][0 0 1 0][0 0 0 1][1 0 0 0][0 0 1 0][1 0 0 0]
%e A321733 .
%e A321733 [0 0 1 0][0 0 1 0][0 0 1 0][0 0 1 0][0 0 1 0][0 0 1 0]
%e A321733 [1 0 0 0][1 0 0 0][0 1 0 0][0 1 0 0][0 0 0 1][0 0 0 1]
%e A321733 [0 1 0 0][0 0 0 1][1 0 0 0][0 0 0 1][1 0 0 0][0 1 0 0]
%e A321733 [0 0 0 1][0 1 0 0][0 0 0 1][1 0 0 0][0 1 0 0][1 0 0 0]
%e A321733 .
%e A321733 [0 0 0 1][0 0 0 1][0 0 0 1][0 0 0 1][0 0 0 1][0 0 0 1]
%e A321733 [1 0 0 0][1 0 0 0][0 1 0 0][0 1 0 0][0 0 1 0][0 0 1 0]
%e A321733 [0 1 0 0][0 0 1 0][1 0 0 0][0 0 1 0][1 0 0 0][0 1 0 0]
%e A321733 [0 0 1 0][0 1 0 0][0 0 1 0][1 0 0 0][0 1 0 0][1 0 0 0]
%t A321733 prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
%t A321733 multsubs[set_,k_]:=If[k==0,{{}},Join@@Table[Prepend[#,set[[i]]]&/@multsubs[Drop[set,i-1],k-1],{i,Length[set]}]];
%t A321733 Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],And[Union[First/@#]==Range[Max@@First/@#]==Union[Last/@#],Total/@prs2mat[#]==Total/@Transpose[prs2mat[#]]]&]],{n,5}]
%Y A321733 Cf. A006052, A007016, A049311, A054976, A057151, A104602, A120732, A319056, A321717, A321723, A321732, A321735, A321736, A321739.
%K A321733 nonn,more
%O A321733 0,3
%A A321733 _Gus Wiseman_, Nov 18 2018
%E A321733 a(7)-a(14) from _Lars Blomberg_, May 23 2019