Evaluate Triple Sum

\[\large \displaystyle \sum _{ n=2 }^{ 2016 }{ \displaystyle \sum _{ k=0 }^{ n }{ \displaystyle \sum _{ j=0 }^{ \phi ( n ) +1 }{ \left(\dbinom nk \dfrac { { ( -1 ) }^{ n+k }{ ( n+k ) }^{ j } }{ ( \phi ( n ) +1 ) ! } \right) } } } = \, ? \]

For your final step of your calculation, you may refer to this list of prime numbers.

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