ordinary generating function

The generating function of a sequence of numbers is a formal power series whose coefficients are the members of that sequence.

A generating function f(x) is a formal power series f(x) = sum_(n = 0)^∞ a_n x^n whose coefficients give the sequence {a_0, a_1, ...}. The Wolfram Language command GeneratingFunction[expr, n, x] gives the generating function in the variable x for the sequence whose nth term is expr. Given a sequence of terms, FindGeneratingFunction[{a1, a2, ...}, x] attempts to find a simple generating function in x whose nth coefficient is a_n.

cumulant-generating function | enumerate | exponential generating function | formal power series | moment-generating function | recurrence relation | subset sum problem | Z-transform

college level