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%I #20 Dec 11 2019 05:04:45
%S 1,1,11,248,9968,638772,60061657,7798036000,1336715859150,
%T 292406145227392,79483340339739367,26280500564448081664,
%U 10386012861097225139356,4834639222955142417477888,2618110215141486526589786501,1631888040186649673361825042432,1159983453675106278249250918734938
%N The permanent of an n X n Toeplitz matrix M(n) whose first row consists of successive positive integer numbers 2*n - 1, n - 1, ..., 1 and whose first column consists of 2*n - 1, 2*n - 2, ..., n.
%C The trace of the matrix M(n) is A000384(n).
%C The sum of the first row of the matrix M(n) is A034856(n).
%C The sum of the first column of the matrix M(n) is A000326(n).
%C For n > 1, the sum of the superdiagonal of the matrix M(n) is A000290(n-1).
%C For n > 1, the sum of the subdiagonal of the matrix M(n) is A001105(n-1).
%H Stefano Spezia, <a href="/A323255/b323255.txt">Table of n, a(n) for n = 0..35</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz matrix</a>
%e For n = 1 the matrix M(1) is
%e 1
%e with permanent a(1) = 1.
%e For n = 2 the matrix M(2) is
%e 3, 1
%e 2, 3
%e with permanent a(2) = 11.
%e For n = 3 the matrix M(3) is
%e 5, 2, 1
%e 4, 5, 2
%e 3, 4, 5
%e with permanent a(3) = 248.
%t b[i_]:=i; a[n_]:=If[n==0, 1, Permanent[ToeplitzMatrix[Join[{b[2*n-1]}, Array[b, n-1, {2*n-2,n }]], Join[{b[2*n-1]},Array[b, n-1, {n-1,1}]]]]]; Array[a, 16, 0]
%o (PARI) tm(n) = {my(m = matrix(n, n, i, j, if (j==1, 2*n-i, n-j+1))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m;}
%o a(n) = matpermanent(tm(n)); \\ _Stefano Spezia_, Dec 11 2019
%Y Cf. A000290, A000326, A000384, A001105, A001792.
%Y Cf. A034856, A204235, A318173, A322908, A322909.
%Y Cf. A323254 (determinant of matrix M(n)).
%K nonn
%O 0,3
%A _Stefano Spezia_, Jan 09 2019
%E a(0) = 1 prepended by _Stefano Spezia_, Dec 08 2019
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