Quite a handful?

Calculus Level 4

\[ \large \left(\sum_{n=0}^\infty \dfrac1{5^n}\dbinom{2n}n \right)^2 = \, ? \]

Notation: \( \binom MN \) denotes the binomial coefficient, \( \binom MN = \frac{M!}{N!(M-N)!} \).

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