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A364791 a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the integers 0, 1, 2, ..., n-1.

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%I A364791 #10 Jan 08 2024 01:09:35
%S A364791 1,2,6,23,120,718,5005,40274,362592,3627920,39909484,478991123
%N A364791 a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the integers 0, 1, 2, ..., n-1.
%H A364791 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%t A364791 a[n_]:=Count[Table[MatrixRank[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n - 1]]], i]]], {i, n!}], n]; Join[{1}, Array[a, 9, 2]] // Flatten
%Y A364791 Right diagonal of A364790.
%Y A364791 Cf. A358323 (minimal determinant), A358324 (maximal determinant), A358326 (minimal permanent), A358327 (maximal permanent).
%K A364791 nonn,hard,more
%O A364791 1,2
%A A364791 _Stefano Spezia_, Aug 08 2023
%E A364791 a(10)-a(12) from _Andrew Howroyd_, Jan 07 2024