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%I #11 Nov 02 2022 11:53:15
%S 1,0,0,1,32,1422,146720,18258864,3217515264,910849979232,
%T 316878962588928,143616562358849280,90359341652805156864,
%U 68004478547050644357120,63187026071337208000512000,75392341069747600992153600000,104962910849766568886449582080000,174017685915978467201007058206720000
%N a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = floor(i*j/3).
%C The matrix M(n) is the n-th principal submatrix of the rectangular array A143974.
%C det(M(0)) = 1, det(M(3)) = -1, and otherwise det(M(n)) = 0.
%e a(5) = 1422:
%e 0 0 1 1 1
%e 0 1 2 2 3
%e 1 2 3 4 5
%e 1 2 4 5 6
%e 1 3 5 6 8
%t a[n_]:=Permanent[Table[Floor[i j/3],{i,n},{j,n}]]; Join[{1},Array[a,17]]
%o (Python)
%o from sympy import Matrix
%o def A358157(n): return Matrix(n,n,[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. A143974.
%Y Cf. A000212 (matrix element M[n,n]), A181286 (trace of M(n)), A358158 (hafnian of M(2*n)).
%K nonn
%O 0,5
%A _Stefano Spezia_, Nov 01 2022