Initially we have 1 red and 1 green ball in a box. At each step we choose a ball randomly from the box, look at its color and then return it in the box with an additional ball of the same color. This way there will be 3 balls in the box after the first step, 4 balls after the second step, and so on. Let X denote the number of red balls in the box after the 1000th step. Find the probability mass function of X.