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%I #32 Jan 24 2024 18:33:14
%S 1,1,2,10,72,624,6522,80178,1129368,17917032,316108752,6138887616,
%T 130120838400,2989026225696,73964789192400,1961487062520720,
%U 55495429438186920,1668498596700706440,53122020640948010640,1785467619718933936560,63175132023953553400440
%N Number of (0,1)-matrices with n ones, no zero rows or columns, and distinct rows and columns.
%H Andrew Howroyd, <a href="/A321446/b321446.txt">Table of n, a(n) for n = 0..50</a>
%e The a(3) = 10 matrices:
%e [1 1] [1 1] [1 0] [0 1]
%e [1 0] [0 1] [1 1] [1 1]
%e .
%e [1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
%e [0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
%e [0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]
%t prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
%t Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],UnsameQ@@prs2mat[#],UnsameQ@@Transpose[prs2mat[#]]]&]],{n,6}]
%o (PARI) \\ Q(m, n, wf) defined in A321588.
%o seq(n)={my(R=vectorv(n,m,Q(m,n,w->1 + y^w + O(y*y^n)))); for(i=2, #R, R[i] -= i*R[i-1]); Vec(1 + vecsum(vecsum(R)))} \\ _Andrew Howroyd_, Jan 24 2024
%Y Cf. A000612, A007716, A049311, A101370, A120733, A135589, A283877, A316980, A319559, A321515, A321586, A321587, A321588, A369285.
%K nonn
%O 0,3
%A _Gus Wiseman_, Nov 13 2018
%E a(7) onwards from _Andrew Howroyd_, Jan 20 2024
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