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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.

%I A359562 #16 Jan 25 2023 18:29:29
%S A359562 1,1,5,54,980,26000,977844,48486480,3168454720,257625275760,
%T A359562 26347709832000,3217348801257888,477582176242255104,
%U A359562 82066363639286366080,16709994767104962690304,3847766849105116759200000,1029727509567022262979280896,306114655769763238348323419392,104188715467117934409088054935552
%N 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.
%H A359562 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%F A359562 A359616(n) <= a(n) <= A359617(n).
%e A359562 a(3) = 54:
%e A359562   [   3,  2*i,   i;
%e A359562    -2*i,    3, 2*i;
%e A359562      -i, -2*i,   3 ]
%t A359562 Join[{1},Table[Permanent[ToeplitzMatrix[Join[{n},I Reverse[Range[n-1]]]]],{n,18}]]
%o A359562 (Python)
%o A359562 from sympy import Matrix, I
%o A359562 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
%Y A359562 Cf. A307783 (symmetric Toeplitz matrix).
%Y A359562 Cf. A359559, A359560, A359561 (determinant).
%Y A359562 Cf. A359616 (minimal), A359617 (maximal).
%K A359562 nonn
%O A359562 0,3
%A A359562 _Stefano Spezia_, Jan 06 2023