A360067 a(n) = det(M) where M is an n X n matrix with M[i,j] = i^j*(i-j).

1, 0, 2, 12, 2304, 898560, 4827340800, 143219736576000, 49230909076930560000, 149334225705682285363200000, 5482643392499167214520238080000000, 2322479608280149573505226859610112000000000, 13283541711093841017468807905468592685056000000000000

Offset: 0

Author

José María Grau Ribas, Jan 24 2023

Keywords

• nonn

Crossrefs

Cf. A060238, A174890, A176005, A176001, A000178, A089064, A152653.

Programs

Maple

a:= n-> LinearAlgebra[Determinant](Matrix(n, (i,j) -> i^j*(i-j))):
seq(a(n), n=0..12);  # Alois P. Heinz, Jan 25 2023

Mathematica

a[n_] := Det@Table[i^j (i - j), {i, n}, {j, n}]; Table[a[n], {n, 1, 15}]

PARI

a(n) = matdet(matrix(n, n, i, j, i^j*(i-j))); \\ Michel Marcus, Jan 24 2023

Python

from sympy import Matrix
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

Formula

For n>=1, a(n) = A000178(n-1) * A089064(n). - Vaclav Kotesovec, Apr 19 2024