What is the generating function of partitions of $n$ into $a_1, \ldots, a_r$ where $a_1 \le \ldots \le a_r$, $a_1 = 1$ and $a_i - a_{i-1} \le 1$ for $2 \le i \le r$?
Hint: find a bijection between set of these partitions and some set of partitions with a well-known generating function.
I've tried to find a bijection using Ferrers diagrams but with no result.