Find the Taylor Series for f(x) centered at $\displaystyle a=11\pi$

f(x) = 4 cos(x)

I got:

$\displaystyle \sum^{\infty}_{n=0} (-1)^n \frac{4(x-11\pi)^{2n}}{(2n)!}$

What did I do wrong on this? I was confused about how to evaluate at $\displaystyle 11\pi$

Since at n=0, I did not get a 0, I didn't think I needed to have (2n+1)