Does series with factorials converge/diverge: $\sum\limits_{n=1}^\infty \frac{4^n n!n!}{(2n)!}$? $$\sum_{n=1}^\infty {{4^n n!n!}\over{(2n)!}}$$
I tried the ratio test but got that the limit is equal to 1, this tells me nothing of whether the series diverges or converges. if I didn't make any errors when doing the ratio test,  it may diverge, but I need help proving that. Is there any other test I could try.

Note that $$\frac{(2n)!}{n!n!}\leq\sum_0^{2n}\binom{2n}{k}=(1+1)^{2n}=4^n$$
So $$\frac{4^n n!n!}{(2n)!}\geq 1$$
