What is the coefficient of x4x^4x4 in the Taylor series of f(x)=e2xf(x) = e^{2x}f(x)=e2x centered at x=0x = 0x=0?
24!=112\frac{2}{4!} = \frac{1}{12}4!2=121
244!=23\frac{2^4}{4!} = \frac{2}{3}4!24=32
4!24=32\frac{4!}{2^4} = \frac{3}{2}244!=23
1624=23\frac{16}{24} = \frac{2}{3}2416=32