Extract from OP-SF NET

From: Victor Alexandrov 
Subject: Open problem

We would like to propose the following problem:

Can the infinite series

$$\sum\limits_{n=1}^{\infty}\frac{x^n}{n!}\ln(n+\alpha)$$

be expressed in terms of known functions and constants?

We do not know any solution of the problem and will be
thankful for any comments, suggestions, solutions, etc.