Given the series   pn=n=1(4n+4)!4nn!\displaystyle \ \ {p}_{{n}}={\sum_{{{n}={1}}}^{\infty}}\frac{{{\left({4}{n}+{4}\right)}!}}{{{4}^{{n}}{n}!}}

Find   limnpn+1pn=\displaystyle \ \ \lim_{{{n}\to\infty}}{\left|{\frac{{{p}_{{{n}+{1}}}}}{{{p}_{{n}}}}}\right|}=