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A358159 a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = i*j - floor(i*j/3).

%I A358159 #10 Nov 02 2022 11:53:28
%S A358159 1,1,7,102,4396,374216,49857920,11344877568,3879729283968,
%T A358159 1804571320405248,1195546731955854336,1058730877124859138048,
%U A358159 1184751018265831288602624,1725335046543668616765112320,3147123030650561978295975936000,6934187745940804400441946931200000,18840570649600136750602236509552640000
%N A358159 a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = i*j - floor(i*j/3).
%C A358159 The matrix M(n) is the n-th principal submatrix of the rectangular array A143976 and it is singular for n > 3.
%e A358159 a(5) = 374216:
%e A358159     1   2   2   3   4
%e A358159     2   3   4   6   7
%e A358159     2   4   6   8  10
%e A358159     3   6   8  11  14
%e A358159     4   7  10  14  17
%t A358159 Join[{1},Table[Permanent[Table[i*j-Floor[i*j/3],{i,n},{j,n}]],{n,17}]]
%o A358159 (Python)
%o A358159 from sympy import Matrix
%o A358159 def A358159(n): return Matrix(n,n,[i*j-i*j//3 for i in range(1,n+1) for j in range(1,n+1)]).per() if n else 1 # _Chai Wah Wu_, Nov 02 2022
%Y A358159 Cf. A143976.
%Y A358159 Cf. A071619 (matrix element M[n,n]), A358042 (trace of M(n)), A358160 (hafnian of M(2*n)).
%K A358159 nonn
%O A358159 0,3
%A A358159 _Stefano Spezia_, Nov 01 2022