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A362073 a(n) is the permanent of the n X n symmetric matrix M(n) whose generic element M[i,j] = digsum(i*j).

%I A362073 #9 Apr 09 2023 14:43:06
%S A362073 1,1,8,216,7344,168183,7226091,506792295,43261224876,5520748306176,
%T A362073 170835815638728,19632554202684096,2228687316428293152,
%U A362073 347514692118635694888,62201193604462666921968,8113764691750577654439864,1557556394182730485102253088,348394812690307787609428395792
%N A362073 a(n) is the permanent of the n X n symmetric matrix M(n) whose generic element M[i,j] = digsum(i*j).
%C A362073 The matrix M(n) is nonsingular only for n = 1, 5, 6 and 7 with determinant equal respectively to 1, 6561, 59049 and -531441.
%F A362073 Sum_{i=1..n} M[n-i+1,i] = A362072(n).
%e A362073 a(6) = 7226091:
%e A362073     [1, 2, 3, 4, 5, 6]
%e A362073     [2, 4, 6, 8, 1, 3]
%e A362073     [3, 6, 9, 3, 6, 9]
%e A362073     [4, 8, 3, 7, 2, 6]
%e A362073     [5, 1, 6, 2, 7, 3]
%e A362073     [6, 3, 9, 6, 3, 9]
%t A362073 M[i_, j_]:=Total[IntegerDigits[i*j]]; Join[{1}, Table[Permanent[Table[M[i, j], {i,  n}, {j, n}]], {n, 18}]]
%o A362073 (PARI) a(n) = matpermanent(matrix(n, n, i, j, sumdigits(i*j))); \\ _Michel Marcus_, Apr 08 2023
%Y A362073 Cf. A003991, A007953, A336225, A353933, A362072, A362074 (rank).
%K A362073 nonn,base
%O A362073 0,3
%A A362073 _Stefano Spezia_, Apr 08 2023