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%I #14 Jul 07 2024 05:46:00
%S 1,0,-1,8,28,282,27495,581268,17344692,1246207300,33366771123
%N a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e a(5) = 282:
%e [0, 3, 4, 2, 1]
%e [3, 0, 3, 4, 2]
%e [4, 3, 0, 3, 4]
%e [2, 4, 3, 0, 3]
%e [1, 2, 4, 3, 0]
%t a[0]=1; a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]],{i,(n-1)!}]]; Array[a,11,0]
%Y Cf. A085750, A358324.
%Y Cf. A085807 (minimal permanent), A374279 (minimal), A374281 (maximal absolute value), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).
%K sign,hard,more
%O 0,4
%A _Stefano Spezia_, Jul 02 2024