Problem

Find the

Using expanded notation for series I can get an answer that matches up with maple:

What I can't seem to do is find this with a closed form notation for series.

My attempt

First I substitute...

Then I try to get everything to be to power of n...

Then I try to get everything to the same index by taking out n=0 elements where necessary...

Using initial conditions:

The recurrence relationship I get is:

But this is wrong because if I plug in n=2, I get

Where did I go wrong?