Square your limit problem

Calculus Level 4

\[\large \lim \limits_{n\to \infty }\sqrt[n]{\dfrac{( 2n) ! }{n! n^{n}} } \]

If the value of the limit above equals to \( A \times e^B \) for integers \(A\) and \(B\), find the value of \(A\times B\).

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