Answer
$c_k=\binom{p}{k}=\dfrac{p(p-1)(p-2)\cdot\cdot\cdot (p-k+1)}{k!}$ for $k=0,1,2,....$
Work Step by Step
Given a function $f$, we can determine the coefficients $c_k$ of the Taylor series centered in $a$ using the formula:
$f(x)=\sum_{k=0}^{\infty} c_k x^k=\sum_{k=0}^{\infty} \binom{p}{k} x^k$
$c_k=\binom{p}{k}=\dfrac{p(p-1)(p-2)\cdot\cdot\cdot (p-k+1)}{k!}$ for $k=0,1,2,....$
