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%I #23 Apr 19 2024 07:11:55
%S 1,0,2,12,2304,898560,4827340800,143219736576000,49230909076930560000,
%T 149334225705682285363200000,5482643392499167214520238080000000,
%U 2322479608280149573505226859610112000000000,13283541711093841017468807905468592685056000000000000
%N a(n) = det(M) where M is an n X n matrix with M[i,j] = i^j*(i-j).
%F For n>=1, a(n) = A000178(n-1) * A089064(n). - _Vaclav Kotesovec_, Apr 19 2024
%p a:= n-> LinearAlgebra[Determinant](Matrix(n, (i,j) -> i^j*(i-j))):
%p seq(a(n), n=0..12); # _Alois P. Heinz_, Jan 25 2023
%t a[n_] := Det@Table[i^j (i - j), {i, n}, {j, n}]; Table[a[n], {n, 1, 15}]
%o (PARI) a(n) = matdet(matrix(n, n, i, j, i^j*(i-j))); \\ _Michel Marcus_, Jan 24 2023
%o (Python)
%o from sympy import Matrix
%o def A360067(n): return Matrix(n,n,[i**j*(i-j) for i in range(1,n+1) for j in range(1,n+1)]).det() # _Chai Wah Wu_, Jan 27 2023
%Y Cf. A060238, A174890, A176005, A176001, A000178, A089064, A152653.
%K nonn
%O 0,3
%A _José María Grau Ribas_, Jan 24 2023