Suppose f(x)=∑n=0∞anxnf(x) = \sum_{n=0}^{\infty} a_n x^nf(x)=∑n=0∞anxn satisfies the differential equation f′(x)=f(x)2f'(x) = f(x)^2f′(x)=f(x)2 with f(0)=1f(0) = 1f(0)=1. What is a2a_2a2?
000
12\frac{1}{2}21
111
14\frac{1}{4}41