I am looking at a certain sequence, and consequently I am wondering if anyone knows if there happens to exist a closed form solution for this sum:
or, an alternate form:
For low values of $a$, Wolfram Alpha gives a closed form in terms of the polygamma function function of order $0$, so I am wondering if there is a general closed form in terms of $a$.
I asked this question on MSE, but have not received answers yet. I realize I did ask it recently there, but I also wanted to ask it here just to see if anyone had seen this sum before.