As the title says, I'm wondering whether there is any known closed-from for the following series:
$$\sum_{k=0}^{\infty} \frac{1}{(k!)!}$$
Here I don't mean the double factorial (treated here) when I'm writing $(k!)!$, but the factorial of the integer $k!$.
Trying on WolframAlpha, I get the funny value $2.501388888888888888888890500626459...$, but no closed-form. If you have any reference which focuses on this number, I would also be interested. I found nothing so far.
Thank you very much!