# A Complicated Binomial Sum

Calculus Level 5

$\large \displaystyle \sum_{n=0}^{\infty} \dbinom{4n}{2n} 32^{-n} = \sqrt{A}\cos\left(\dfrac{\pi}{B}\right)$

If the equation above holds true for positive integers $$A$$ and $$B$$, then find $$A\times B$$.

 Notation: $$\dbinom nk = \dfrac{n!}{k!(n-k)!}$$ denotes the binomial coefficient.

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