1. The problem statement, all variables and given/known data Find the Taylor series for 0.5x^2[e^x-e^(-x)] around x=0. What is the coefficient of x^n? 2. Relevant equations e^x=∑x^n/n! 3. The attempt at a solution I understand how to find the Taylor series for this equation (it being ∑[x^(2n+3)/n!]; x^3+x^5+x^7/2!+...) through manipulation of the Taylor series for e^x; however I'm not quite sure what it means by the "coefficient of x^n?" The answer is apparently 0 when n is 1 or even, and otherwise it is given by 1/[(n-3)/2]!, but how is this found? Thank you so much for any help!