i'm looking for an apper bound to the following integral or equivalent when $n$ leads to $ +\infty $ to the following expression

$I_n:=|\int_{0}^1 \int_{0}^1 \frac{p_n(x) p_n(y)}{(1-xy)} dx dy | $ with $ p_n(t):=\frac{1}{n!}(t^n(1-t)^n)^{(n)}$. This integral is similar to beukers integral; after integrating $n$ times to $y$ ,i obtain
$I_n:=|\int_{0}^1 \int_{0}^1 \frac{p_n(x) x^n y^n(1-y)^n}{(1-xy)^{(n+1)}} dx dy | $, i don't know what to do after since i can't have interesting expression inside the integral when i derive n times $x$ .