In this ocassion we consider the followgin series that involve ${n\brace k}$ the Stirling number of the second kind and $(n)_k$ the Pochhammer symbols. I've known from an informative point of view that in the literature was explored an example versus the definition of irrational absolutely abnormal numbers (for example from [1]).

This is the Wikipedia article dedicated to *Normal number*.

I wondered as curiosity if in the context of these definitions, the definitions and notions concerning normal numbers it is possible to propose some statement or conjecture about the following series

$$\sum_{n=1}^\infty\frac{1}{{2n\brace n}^{{2n\brace n}}} \tag{1}$$ or $$\sum_{n=1}^\infty \frac{1}{(2n)_{n}^{(2n)_{n}}}.\tag{2}$$

Question.Show heuristics/reasonings, or set a proposition or propose a conjecture concerning the series $(1)$ or $(2)$ in the context of the normal numbers.Many thanks.

I hope that my series and question have a good mathematical content and it makes good sense in the context of the theory of number numbers.

## References:

[1] Glyn Harman, *One Hundred Years of Normal Numbers*, proceeding from Number Theory for the Millennium II, A K Peters (2002).