structural:reformatting
Ordinary generating function (OGF)

When the term generating function is used without qualification, it is usually taken to mean an ordinary generating function. The ordinary generating function of a sequence a is: G (a n; x) = ∑ n = 0 ∞ a n x n. {\displaystyle G(a_{n};x)=\sum _{n=0}^{\infty }a_{n}x^{n}.} If a is the probability mass function of a discrete random variable, then its ordinary generating function is called a probability-generating function.