Binomially Amazing! 4

\[\large \sum _{ n=0 }^{ 1729 }{ { \left( n-\frac { 1729 }{ 2 } \right) }^{ 2 }\left( \begin{matrix} 1729 \\ n \end{matrix} \right) { \left( \frac { 1 }{ 2 } \right) }^{ 1729 }=\frac { A }{ B } } \]

Find: \(A+B\)

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