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A358161 a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ceiling(i*j/3).

%I A358161 #11 Nov 02 2022 11:53:33
%S A358161 1,1,3,19,434,18142,1138592,131646240,22247821152,4990553682336,
%T A358161 1661493079305216,729074911776673536,397903630707426852864,
%U A358161 290086114501734871449600,262660633302518916820992000,284075108357948520100761600000,385808192325346588875691868160000,626209817056857125529475382231040000
%N A358161 a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ceiling(i*j/3).
%C A358161 The matrix M(n) is the n-th principal submatrix of the rectangular array A143977.
%C A358161 det(M(n)) = 1 for n <= 3, and otherwise det(M(n)) = 0.
%e A358161 a(5) = 18142:
%e A358161     1  1  1  2  2
%e A358161     1  2  2  3  4
%e A358161     1  2  3  4  5
%e A358161     2  3  4  6  7
%e A358161     2  4  5  7  9
%t A358161 a[n_]:=Permanent[Table[Ceiling[i j/3],{i,n},{j,n}]]; Join[{1},Array[a,17]]
%o A358161 (Python)
%o A358161 from fractions import Fraction
%o A358161 from sympy import Matrix
%o A358161 def A358161(n): return Matrix(n,n,[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 A358161 Cf. A143977.
%Y A358161 Cf. A008810 (matrix element M[n,n]), A070333 (trace of M(n+1)), A358162 (hafnian of M(2*n)).
%K A358161 nonn
%O A358161 0,3
%A A358161 _Stefano Spezia_, Nov 01 2022