# Partitions with no 1s

Probability Level 2

\begin{aligned} p(17) &= 297 \\ p(18) &= 385 \\ p(19) &= 490 \\ p(20) &= 627 \\ p(21) &= 792 \end{aligned}

Let $p(n)$ be the number of partitions of an integer $n$. The values of $p(17), p(18),p(19),p(20), p(21)$ are as shown above.

How many partitions of 20 are there that do not contain any parts equal to 1?

×