Radius of convergence?

[n1nja_b0ss]

I have the following infinite sum and I need to find its radius of convergence, but have no idea where to start from as the sum itself is way too complicated for me:

 

[HallsofIvy]

Do you know the "ratio test" for

 

[Steven G]

factorials think ratio test.

 

[HallsofIvy]

I didn't know factorials could think!