Binomially Amazing! #2

Calculus Level 5

\[\sum _{ r=0 }^{ 1729 }{ \frac { { \left( -1 \right) }^{ r }\left( \begin{matrix} 1729 \\ r \end{matrix} \right) }{ 4r+2 } } ={ 2 }^{ a }\frac { { \left( b! \right) }^{ c } }{ \left( d! \right) } \]

The equation above holds true for integers \(a,b,c\) and \(d\). Find the value of \(a+b+c+d\),

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