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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.
6
1, 1, 5, 54, 980, 26000, 977844, 48486480, 3168454720, 257625275760, 26347709832000, 3217348801257888, 477582176242255104, 82066363639286366080, 16709994767104962690304, 3847766849105116759200000, 1029727509567022262979280896, 306114655769763238348323419392, 104188715467117934409088054935552
OFFSET
0,3
FORMULA
A359616(n) <= a(n) <= A359617(n).
EXAMPLE
a(3) = 54:
[ 3, 2*i, i;
-2*i, 3, 2*i;
-i, -2*i, 3 ]
MATHEMATICA
Join[{1}, Table[Permanent[ToeplitzMatrix[Join[{n}, I Reverse[Range[n-1]]]]], {n, 18}]]
PROG
(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
CROSSREFS
Cf. A307783 (symmetric Toeplitz matrix).
Cf. A359559, A359560, A359561 (determinant).
Cf. A359616 (minimal), A359617 (maximal).
Sequence in context: A304322 A132619 A251583 * A359617 A376095 A223896
KEYWORD
nonn
AUTHOR
Stefano Spezia, Jan 06 2023
STATUS
approved