login
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).
2

%I #10 Nov 02 2022 11:53:28

%S 1,1,7,102,4396,374216,49857920,11344877568,3879729283968,

%T 1804571320405248,1195546731955854336,1058730877124859138048,

%U 1184751018265831288602624,1725335046543668616765112320,3147123030650561978295975936000,6934187745940804400441946931200000,18840570649600136750602236509552640000

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

%e a(5) = 374216:

%e 1 2 2 3 4

%e 2 3 4 6 7

%e 2 4 6 8 10

%e 3 6 8 11 14

%e 4 7 10 14 17

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

%o (Python)

%o from sympy import Matrix

%o 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 Cf. A143976.

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

%K nonn

%O 0,3

%A _Stefano Spezia_, Nov 01 2022