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A332566 a(n) is the permanent of an n X n symmetric Toeplitz matrix M(n) whose first row consists of a single zero followed by successive positive integers repeated (A004526).

%I A332566 #14 Aug 19 2021 02:32:32
%S A332566 1,0,1,2,16,150,2333,45840,1227816,40715300,1701223409,84902728550,
%T A332566 5108474886424,357837483830570,29336856811970045,2745407159100236484,
%U A332566 294324995624694053072,35473014438701226021416,4818705384665419284918401,727012502373285844943278058,122057159014198483893887865744
%N A332566 a(n) is the permanent of an n X n symmetric Toeplitz matrix M(n) whose first row consists of a single zero followed by successive positive integers repeated (A004526).
%H A332566 Vaclav Kotesovec, <a href="/A332566/b332566.txt">Table of n, a(n) for n = 0..35</a>
%H A332566 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_matrix">Symmetric matrix</a>
%H A332566 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e A332566 For n = 4 the matrix M(4) is
%e A332566     0 1 1 2
%e A332566     1 0 1 1
%e A332566     1 1 0 1
%e A332566     2 1 1 0
%e A332566 with permanent a(4) = 16.
%t A332566 nmax:=20; k[i_]:=Floor[i/2];a[n_]:=If[n==0,1,Permanent[ToeplitzMatrix[Array[k, n], Array[k, n]]]]; Table[a[n],{n,0,nmax}]
%o A332566 (PARI) tm(n) = {my(m = matrix(n, n, i, j, if (i==1, floor(j/2), if (j==1, floor(i/2))))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m; }
%o A332566 a(n) = matpermanent(tm(n));
%Y A332566 Cf. A004526, A083392, A331491, A333119.
%K A332566 nonn
%O A332566 0,4
%A A332566 _Stefano Spezia_, Feb 16 2020