Binomial sufficiency

\[\large\ \sum _{ { k=0 } }^{1008} { { \left( 2k+1 \right) } } ^{ 2 }{2017\choose{2k+1}}= a(a + 1)2^b\]

Above sum can be represented for positive integers \(a, b\).

Find \(a + b\).

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