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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
1, 2, 5, 24, 120, 719, 5040, 40317, 362874, 3628798
OFFSET
1,2
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
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Jul 14 2023
STATUS
approved