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A364231 a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the integers 1, 2, ..., n.

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%I A364231 #12 Dec 30 2023 23:04:38
%S A364231 1,2,6,24,120,718,5005,40274,362604,3627915,39909566,478991256
%N A364231 a(n) is the number of n X n nonsingular symmetric Toeplitz matrices using all the integers 1, 2, ..., n.
%H A364231 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%t A364231 a[n_]:=Count[Table[MatrixRank[ToeplitzMatrix[Part[Permutations[Range[n]],i]]],{i,n!}],n]; Array[a,8]
%Y A364231 Right diagonal of A364230.
%Y A364231 Cf. A350953 (minimal determinant), A350954 (maximal determinant), A351019 (minimal permanent), A351020 (maximal permanent), A356865 (minimal nonzero absolute value determinant).
%K A364231 nonn,hard,more
%O A364231 1,2
%A A364231 _Stefano Spezia_, Jul 14 2023
%E A364231 a(10)-a(12) from _Andrew Howroyd_, Dec 30 2023