I'm trying to order some numbers....For n very large, I need to order:

2^n, 4^n, 2^(n^2), n!, and n^n

I know 2^n<4^n<n^n, but I'm not sure where the 2^(n^2) and the n! come in...I want to say it goes 2^n<4^n<2^(n^2)<n!<n^n, but I'm not too sure.

Is this correct?