Apéry's Constant in terms of Central Binomial Coefficients

Theorem
Apéry's constant can be expressed in terms of binomial coefficients as:


 * $\map \zeta 3 = \ds \dfrac 5 2 \sum_{n \mathop = 1}^\infty \dfrac {\paren {-1}^{n - 1} } {n^3 \dbinom {2 n} n}$