\[\int_{0}^{\infty}\!\!\int_{t}^{\infty}\!\!\!\!\cdots\int_{t}^{\infty}%
\operatorname{Ai}\left({-}t\right)(\,\mathrm{d}t)^{n}=\frac{2\cos\left(\tfrac{%
1}{3}(n-1)\pi\right)}{3^{(n+2)/3}\Gamma\left(\tfrac{1}{3}n+\tfrac{2}{3}\right)},\]