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).

1, 1, 7, 102, 4396, 374216, 49857920, 11344877568, 3879729283968, 1804571320405248, 1195546731955854336, 1058730877124859138048, 1184751018265831288602624, 1725335046543668616765112320, 3147123030650561978295975936000, 6934187745940804400441946931200000, 18840570649600136750602236509552640000

Offset: 0

Author

Stefano Spezia, Nov 01 2022

Keywords

• nonn

Comments

The matrix M(n) is the n-th principal submatrix of the rectangular array A143976 and it is singular for n > 3.

Examples

			a(5) = 374216:
    1   2   2   3   4
    2   3   4   6   7
    2   4   6   8  10
    3   6   8  11  14
    4   7  10  14  17
		

Crossrefs

Cf. A143976.

Cf. A071619 (matrix element M[n,n]), A358042 (trace of M(n)), A358160 (hafnian of M(2*n)).

Programs

Mathematica

Join[{1},Table[Permanent[Table[i*j-Floor[i*j/3],{i,n},{j,n}]],{n,17}]]

Python

from sympy import Matrix
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