  Let $s \geq 3$ be a fixed positive integer and $a_1,\dots,a_s \in \mathbb{Z}$
be arbitrary. We show that, on average over $k$, the density of numbers
represented by the degree $k$ diagonal form \[ a_1 x_1^k + \cdots + a_s x_s^k
\] decays rapidly with respect to $k$.
