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Closed form for $\prod_{1 \leq i < j \leq k} (j - i)$?
Is there a closed form for $\prod_{1 \leq i < j \leq k} (j - i)$? It looks like something like a determinant of a Vandermonde matrix, but I can't seem to get it to fit.
4
votes
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Closed form expression for a product.
A simple method for evaluating a product is term cancellation. For example, the product
$$\begin{align*}
\prod_{k=2}^{n}\left(1-\frac{1}{k}\right)&=\prod_{k=2}^{n}\left(\frac{k-1}{k}\right)\\
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