The Clarkkkkson, denoted ¥, is a dynamic googologism that grows over time, based on the lynz. Let \(n!\) represent the factorial, and create the following extension: * \(n!! = n! \cdot (n - 1)! \cdot (n - 2)! \cdot (n - 3)! \cdot \ldots\) * \(n!!! = n!! \cdot (n - 1)!! \cdot (n - 2)!! \cdot (n - 3)!! \cdot \ldots\) * \(n!!!! = n!!! \cdot (n - 1)!!! \cdot (n - 2)!!! \cdot (n - 3)!!! \cdot \ldots\) * etc. For the sake of this article, \(n!!\) will be abbreviated as \(n!2\), \(n!!!\) as \(n!3\), and so forth. The notation is due to Aalbert Torsius. Finally, define the following series: