Is there a free online computer calculator that is more powerful than wolframalpha.com?
There are absolutely huge numbers involved in this calculation, no wonder you won't get the result by simple numerical computation.

However,

Let $x = 52!$ and $y=3.1536\times 10^{16}$. 

A crude lower bound yields:
$$ \frac{\prod_{i=1}^y(x-i)}{x^y} \geq (1 - \frac{y}{x})^y \geq 1-\frac{y^2}{x} .$$
Putting numerical values and wandering on the safe side of approximations you get:
$$1-\frac{y^2}{X} \geq 1-10^{-34}$$.

Thus,

$$ 1-10^{-34} \leq \frac{\prod_{i=1}^y(x-i)}{x^y} \leq 1 $$.

The value you are looking for is basically $1$.