Delicate Derivative Derivation (Posted on 2009-12-18)

F(x) is a function which is defined as F(x) = (x+1)^{2} * e^{2x}. The fiftieth derivative of F(x) with respect to x at x=0, i.e. F^{(50)}(0), is expressible in the form k*2^{n} where k is an odd integer and n is a positive integer.