Ouch

$\large 2^A = \sum_{n=0}^{2016} \left[ (-1)^{n(n-1)/2} \times 3^{\lfloor n/2 \rfloor } \times \dbinom {2016} n\right ]$

What is the value of $A$ ?

Notations :

• $\lfloor \cdot \rfloor$ denotes the floor function .

• $\dbinom MN$ denotes the binomial coefficient , $\dbinom MN = \dfrac{M!}{N!(M-N)!}$ .