Can someone help me to prove this propertie of Legendre Polynomials?

[User13587]

I already prove other properties of the Legendre polynomials, like:

$$P_n(-x) = (-1)^nP_n(x)$$$$P_{2n+1}(0) = 0$$$$P_n(\pm1)= (\pm1)^n$$
But I can't get this:

$$P_{2n}(0) = \frac{(-1)^n(2n-1)!}{2^{2n-1}((n-1)!)^2}$$

I'm so glad if someone can help me with this.