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).

1, 0, 1, 2, 16, 150, 2333, 45840, 1227816, 40715300, 1701223409, 84902728550, 5108474886424, 357837483830570, 29336856811970045, 2745407159100236484, 294324995624694053072, 35473014438701226021416, 4818705384665419284918401, 727012502373285844943278058, 122057159014198483893887865744

Offset: 0

Author

Stefano Spezia, Feb 16 2020

Keywords

• nonn

Examples

			For n = 4 the matrix M(4) is
    0 1 1 2
    1 0 1 1
    1 1 0 1
    2 1 1 0
with permanent a(4) = 16.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..35
• Wikipedia, Symmetric matrix
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A004526, A083392, A331491, A333119.

Programs

Mathematica

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}]

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; }
a(n) = matpermanent(tm(n));