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 A321735 #4 Nov 19 2018 07:22:23
%S A321735 1,1,2,7,30,153,939,6653,53743,486576
%N A321735 Number of (0,1)-matrices with sum of entries equal to n, no zero rows or columns, weakly decreasing row and column sums, and the same row sums as column sums.
%F A321735 Let c(y) be the coefficient of m(y) in e(y), where m is monomial symmetric functions and e is elementary symmetric functions. Then a(n) = Sum_{|y| = n} c(y).
%e A321735 The a(3) = 7 matrices:
%e A321735 [1 1]
%e A321735 [1 0]
%e A321735 .
%e A321735 [1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
%e A321735 [0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
%e A321735 [0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]
%t A321735 prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
%t A321735 Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],And[Union[First/@#]==Range[Max@@First/@#]==Union[Last/@#],OrderedQ[Total/@prs2mat[#]],OrderedQ[Total/@Transpose[prs2mat[#]]],Total/@prs2mat[#]==Total/@Transpose[prs2mat[#]]]&]],{n,5}]
%Y A321735 Cf. A000700, A007016, A049311, A054976, A057151, A104602, A320451, A321719, A321723, A321732, A321733, A321736, A321739.
%K A321735 nonn,more
%O A321735 0,3
%A A321735 _Gus Wiseman_, Nov 18 2018