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a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ceiling(i*j/3).
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%I #11 Nov 02 2022 11:53:33

%S 1,1,3,19,434,18142,1138592,131646240,22247821152,4990553682336,

%T 1661493079305216,729074911776673536,397903630707426852864,

%U 290086114501734871449600,262660633302518916820992000,284075108357948520100761600000,385808192325346588875691868160000,626209817056857125529475382231040000

%N 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 The matrix M(n) is the n-th principal submatrix of the rectangular array A143977.

%C det(M(n)) = 1 for n <= 3, and otherwise det(M(n)) = 0.

%e a(5) = 18142:

%e 1 1 1 2 2

%e 1 2 2 3 4

%e 1 2 3 4 5

%e 2 3 4 6 7

%e 2 4 5 7 9

%t a[n_]:=Permanent[Table[Ceiling[i j/3],{i,n},{j,n}]]; Join[{1},Array[a,17]]

%o (Python)

%o from fractions import Fraction

%o from sympy import Matrix

%o 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 Cf. A143977.

%Y Cf. A008810 (matrix element M[n,n]), A070333 (trace of M(n+1)), A358162 (hafnian of M(2*n)).

%K nonn

%O 0,3

%A _Stefano Spezia_, Nov 01 2022