I need to use Stirling's Formula to find a value λ so that

(4n)!/ ((2n)!)^2 ~ (λ/√n)(16)^n as n → ∞

So far I have calculated

(√(8πn)(4n/e)^4n)/ (√(4πn)(2n/e)^2n)^2

= (√8πn)/4πn

At which point I get stuck.

Can anyone tell me whether I'm on the right track or not and where to go from here. Much appreciated.