A364229 a(n) is the number of n X n nonsingular Hermitian Toeplitz matrices using all the integers 1, 2, ..., n and with all off-diagonal elements purely imaginary.

1, 2, 5, 24, 120, 719, 5040, 40317, 362874, 3628798

Offset: 1

Author

Stefano Spezia, Jul 14 2023

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Toeplitz Matrix

Crossrefs

Right diagonal of A364228.

Cf. A359614 (minimal determinant), A359615 (maximal determinant), A359616 (minimal permanent), A359617 (maximal permanent).

Programs

Mathematica

a[n_]:=Count[Flatten[Table[MatrixRank[ToeplitzMatrix[Join[{d}, I Part[Permutations[Drop[Range[n], {d}]], i]]]],{i,(n-1)!},{d,n}]],n]; Array[a,9]