Yeah, Binomial King is here.

Algebra Level 3

\[\left( 3 + { x }^{ 2015 } + { x }^{ 2017 } \right)^{ 2016 } = { a }_{ 0 } + { a }_{ 1 }x + { a }_{ 2 }{ x }^{ 2 } + ... + { a }_{ n }{ x }^{ n }\]

Given the above, find the value of

\[{ a }_{ 0 } - \frac { 1 }{ 2 } { a }_{ 1 } - \frac { 1 }{ 2 } { a }_{ 2 } + { a }_{ 3 } - \frac { 1 }{ 2 } { a }_{ 4 } - \frac { 1 }{ 2 } { a }_{ 5 } + { a }_{ 6 }+...\]

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