MathCastle
Counting & ProbabilityEasyRecursion, Catalan Numbers & Generating Functions

Recursion, Catalan Numbers & Generating Functions · Easy problem

The number of ways to make nn cents with pennies and nickels has generating function 1(1−x)(1−x5)\dfrac{1}{(1-x)(1-x^5)}. Find the coefficient of x5x^5 (the number of ways to make 55 cents).