Coefficient of x^50 in the cube of a summation

Question

What is the coefficient of $x^{50}$ in $(\sum_{n=1}^{\inf} x^n)^3$ ?

Does there exist a combinatorial approach to this problem?

Answer 1

The coefficient you desire counts the number of ways to put $50$ indistinguishable balls into $3$ distinguishable boxes, with no empty box. This is a classic stars and bars problem, whose answer is

$$\binom{49}{2}$$