MathCastle
Counting & ProbabilityMediumRecursion, Catalan Numbers & Generating Functions

Recursion, Catalan Numbers & Generating Functions · Medium problem

In the expansion 1(1−x)3=∑n≥0(n+22)xn\dfrac{1}{(1-x)^3}=\sum_{n\ge0}\binom{n+2}{2}x^n, find the coefficient of x4x^4.