Δ(x_1, ..., x_n) | congruent | left bracketing bar 1 | x_1 | x_1^2 | ... | x_1^(n - 1) 1 | x_2 | x_2^2 | ... | x_2^(n - 1) ⋮ | ⋮ | ⋮ | ⋱ | ⋮ 1 | x_n | x_n^2 | ... | x_n^(n - 1) right bracketing bar | = | product_(i, j i>j)(x_i - x_j) (Sharpe 1987). For integers a_1, ..., a_n, Δ(a_1, ..., a_n) is divisible by product_(i = 1)^n(i - 1)!, the first few values of which are the superfactorials 1, 1, 2, 12, 288, 34560, 24883200, 125411328000, ... (OEIS A000178).

superfactorial | Vandermonde matrix

Alexandre-Théophile Vandermonde