Let $X$ be a D11: Set.
The hyperpower set sequence of $X$ is the D62: Sequence \begin{equation} X, \quad \mathcal{P} X, \quad \mathcal{P} \mathcal{P} X, \quad \mathcal{P} \mathcal{P} \mathcal{P} X, \quad \ldots \end{equation}