In probability theory, a member of the class of distributions is any distribution of a discrete random variable N whose values are nonnegative integers whose probability mass function satisfies the recurrence formula p k p k − 1 = a + b k, k = 1, 2, 3, … {\displaystyle {\frac {p_{k}}{p_{k-1}}}=a+{\frac {b}{k}},\qquad k=1,2,3,\dots } for some real numbers a and b, where p k = P {\displaystyle p_{k}=P}. Wikipedia