Suppose P(x)=x^{2016}+a_{2015} x^{2015}+\ldots+a_{1} x+a_{0} satisfies
P(x) P(2 x+1)=P(-x) P(-2 x-1)
for all x \in \mathbb{R}. Find the sum of all possible values of a_{2015}.
Suppose P(x)=x^{2016}+a_{2015} x^{2015}+\ldots+a_{1} x+a_{0} satisfies
for all x \in \mathbb{R}. Find the sum of all possible values of a_{2015}.