Problem 1168 (difficulty: 8/10)

Let \(\displaystyle p_n\) be the number of partitions of the number \(\displaystyle n\) into different parts. For example \(\displaystyle p_0=1\) and \(\displaystyle p_6=4\), because \(\displaystyle 6=5+1=4+2=3+2+1\).) Using the generating series \(\displaystyle P(x)=\sum\limits_{n=0}^\infty p_nx^n\) find an upper bound for \(\displaystyle p_n\).

Give me another random problem!