A359562 a(n) is the permanent of an n X n Hermitian Toeplitz matrix whose first row consists of n, (n-1)*i, (n-2)*i, ..., 3*i, 2*i, i, where i denotes the imaginary unit.

1, 1, 5, 54, 980, 26000, 977844, 48486480, 3168454720, 257625275760, 26347709832000, 3217348801257888, 477582176242255104, 82066363639286366080, 16709994767104962690304, 3847766849105116759200000, 1029727509567022262979280896, 306114655769763238348323419392, 104188715467117934409088054935552

Offset: 0

Author

Stefano Spezia, Jan 06 2023

Keywords

• nonn

Examples

			a(3) = 54:
  [   3,  2*i,   i;
   -2*i,    3, 2*i;
     -i, -2*i,   3 ]
		

Links

• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A307783 (symmetric Toeplitz matrix).

Cf. A359559, A359560, A359561 (determinant).

Cf. A359616 (minimal), A359617 (maximal).

Programs

Mathematica

Join[{1},Table[Permanent[ToeplitzMatrix[Join[{n},I Reverse[Range[n-1]]]]],{n,18}]]

Python

from sympy import Matrix, I
def A359562(n): return Matrix(n,n,[(n+j-i if i>j else j-i-n) if i!=j else n*I for i in range(n) for j in range(n)]).per()*(1,-I,-1,I)[n&3] if n else 1 # Chai Wah Wu, Jan 25 2023

Formula

A359616(n) <= a(n) <= A359617(n).