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

1,2

Links

Table of n, a(n) for n=1..10.

Wikipedia, Toeplitz Matrix

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]

Crossrefs

Right diagonal of A364228.

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

Sequence in context: A322897 A284230 A374926 * A374621 A052111 A176473

Adjacent sequences: A364226 A364227 A364228 * A364230 A364231 A364232

Keyword

nonn,hard,more

Author

Stefano Spezia, Jul 14 2023

Status

approved