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A358163 a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = i*j - ceiling(i*j/3).

%I A358163 #10 Nov 02 2022 11:53:20
%S A358163 1,0,1,30,1272,113224,18615680,4299553536,1507609286784,
%T A358163 781464165813504,525599814806986752,473934337123421786112,
%U A358163 567876971785035135320064,837723761443461191423754240,1549608938859438129393893376000,3582000047767392376356107059200000,9838495669776145718724862743674880000
%N A358163 a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = i*j - ceiling(i*j/3).
%C A358163 The matrix M(n) is the n-th principal submatrix of the rectangular array A143979.
%C A358163 det(M(0)) = 1, det(M(2)) = -1, det(M(3)) = 2, and otherwise det(M(n)) = 0.
%e A358163 a(5) = 113224:
%e A358163     0  1   2   2   3
%e A358163     1  2   4   5   6
%e A358163     2  4   6   8  10
%e A358163     2  5   8  10  13
%e A358163     3  6  10  13  16
%t A358163 a[n_]:=Permanent[Table[i*j-Ceiling[i*j/3],{i,n},{j,n}]]; Join[{1},Array[a,16]]
%o A358163 (Python)
%o A358163 from fractions import Fraction
%o A358163 from sympy import Matrix
%o A358163 def A358163(n): return Matrix(n,n,[i*j-Fraction(i*j,3).__ceil__() 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 A358163 Cf. A143979.
%Y A358163 Cf. A030511 (matrix element M[n-1,n-1]), A358164 (hafnian of M(2*n)).
%K A358163 nonn
%O A358163 0,4
%A A358163 _Stefano Spezia_, Nov 01 2022