Hi all, anyone knows how to obtain an appropriate upper bound for the following product: $\displaystyle \prod_{i=1}^{a}(a-i+1)^{(a-i+1)}$ Many thanks in advance!
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Originally Posted by oscaralive Hi all, anyone knows how to obtain an appropriate upper bound for the following product: $\displaystyle \prod_{i=1}^{a}(a-i+1)^{(a-i+1)}$ Many thanks in advance! For example (assuming the notation is standard and $\displaystyle a\in\mathbb{N}$: $\displaystyle \displaystyle{\prod\limits_{i=1}^{a}(a-i+1)^{(a-i+1)}=a^a\cdot (a-1)^{a-1}\cdot\ldots\cdot 2^2\cdot 1\leq a^{\frac{a(a+1)}{2}}}$
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