own inequality

[win1234]

ให้ $n\in \mathbb{N} $ จงพิสูจน์ว่า
$$\frac{(n!)^2}{[1!2!3!...(n-1)!]^{\frac{2}{n} }} < \frac{(2^n)[(2n+1)(2n+3)(2n+5)...(4n-1)]}{(2n)!} $$