Statement about factorials that I don't understand

[Ertosthnes]

I was reading and came across this statement:

If t > 2n^2 is an integer, then t! > (n^2)^(t-n^2)

I'm not sure why it is true. I don't know what equations are relevant. My feeling is that you don't need anything more than algebra, but perhaps it would also follow from the gamma function or stirling's formula. Can anyone help me out?

 

[quantumdude]

Have you tried to prove it by induction?