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A321720 Number of non-normal (0,1) semi-magic squares with sum of entries equal to n.

%I A321720 #30 Apr 11 2020 17:19:57
%S A321720 1,1,2,6,25,120,726,5040,40410,362881,3630840,39916800,479069574,
%T A321720 6227020800,87181402140,1307674370040,20922977418841,355687428096000,
%U A321720 6402388104196400,121645100408832000,2432903379962038320,51090942171778378800,1124000886592995642000,25852016738884976640000
%N A321720 Number of non-normal (0,1) semi-magic squares with sum of entries equal to n.
%C A321720 A non-normal semi-magic square is a nonnegative integer matrix with row sums and column sums all equal to d, for some d|n.
%H A321720 Andrew Howroyd, <a href="/A321720/b321720.txt">Table of n, a(n) for n = 0..180</a>
%H A321720 Wikipedia, <a href="https://en.wikipedia.org/wiki/Magic_square">Magic square</a>
%H A321720 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%F A321720 a(p) = p! for p prime as the squares are all permutation matrices of order p and a(n) >= n! for n > 1 (see comments in A321717 and A321719). - _Chai Wah Wu_, Jan 13 2019
%F A321720 a(n) = Sum_{d|n, d<=n/d} A008300(n/d, d) for n > 0. - _Andrew Howroyd_, Apr 11 2020
%t A321720 prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
%t A321720 Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],And[Union[First/@#]==Union[Last/@#]==Range[Max@@First/@#],SameQ@@Total/@prs2mat[#],SameQ@@Total/@Transpose[prs2mat[#]]]&]],{n,5}]
%Y A321720 Cf. A006052, A007016, A057151, A068313, A008300, A101370, A104602, A120732, A271103, A319056, A319616.
%Y A321720 Cf. A321717, A321719, A321722, A321723.
%K A321720 nonn
%O A321720 0,3
%A A321720 _Gus Wiseman_, Nov 18 2018
%E A321720 a(7) from _Chai Wah Wu_, Jan 13 2019
%E A321720 a(8)-a(15) from _Chai Wah Wu_, Jan 14 2019
%E A321720 a(16)-a(21) from _Chai Wah Wu_, Jan 16 2019
%E A321720 Terms a(22) and beyond from _Andrew Howroyd_, Apr 11 2020