TITLE: Find coefficient of $x^{50}$ in $(\sum_{i=1}^{\infty}x^n)^3$
QUESTION [6 upvotes]: How do you find the coefficient of $x^{50}$ in $(\sum_{i=1}^{\infty}x^n)^3$?

REPLY [4 votes]: Another way to look at this is purely combinatorial: the number of integer solutions to:
$$a_1+a_2+a_3=50;\quad a_1,a_2,a_3>0.$$
(Or, equivalently, the number of ways to put 50 balls into 3 urns such that no urn is left empty.)
That number is well-known to be $\binom{50-1}{3-1}$.