# Math Help - upper bound for a product

1. ## upper bound for a product

Hi all,
anyone knows how to obtain an appropriate upper bound for the following product:

$\prod_{i=1}^{a}(a-i+1)^{(a-i+1)}$

$\prod_{i=1}^{a}(a-i+1)^{(a-i+1)}$
For example (assuming the notation is standard and $a\in\mathbb{N}$:
$\displaystyle{\prod\limits_{i=1}^{a}(a-i+1)^{(a-i+1)}=a^a\cdot (a-1)^{a-1}\cdot\ldots\cdot 2^2\cdot 1\leq a^{\frac{a(a+1)}{2}}}$