%I #5 Mar 30 2012 17:36:40
%S 1,-10,260,-9002,391860,-20256038,1211950740,-82281893850,
%T 6247844526420,-524546069736150,48243794823724500,
%U -4823577417987578250,520903033165862392500,-60422912433611865159750,7492466897219978346172500
%N Determinant of a certain n X n matrix whose elements are the integers 1 to n^2.
%C Fill the main diagonal, then come back up the adjacent diagonal, skip over to the other adjacent diagonal and precede with 2n through 3n-2, etc.
%e Matrix of order 4 is:
%e 1 8 13 16
%e 7 2 9 14
%e 12 6 3 10
%e 15 11 5 4
%o (PARI) {init_m(n)= m=matrix(n,n,row,col,row*(row==col)); next_entry=n+1; for(i=2,n, col=n-i+1; forstep(row=n,i,-1, m[row,col]=next_entry; next_entry++; col--); col=i; for(row=1,n-i+1, m[row,col]=next_entry; next_entry++; col++))} for(n=1,15, init_m(n); print1(matdet(m),",")) (Rick L. Shepherd)
%K sign
%O 1,2
%A _Robert G. Wilson v_, Jun 16 2003
%E Corrected by _Rick L. Shepherd_, Jun 12 2004