a_n = \left\{
\begin{array}{cll}
2^{n^2} \!\!\!\!\! & , & (\exists \, k \in \mathbb{N}) \, n = k! \\
0 \!\!\!\!\! & , & (\forall \, k \in \mathbb{N}) \, n \neq k!
\end{array} \right.