Finding the inverse Z transform of a signal

[MiZZiTDK]

Hi guys! I am having a problem in finding the inverse z transform of the given signal. Can anyone help me? I'd appreciate it. Thanks!

Here is basically what I did:

However, I don't know what to do next. What is the next thing to do? Thanks!

 

[rude man]

Hi guys! I am having a problem in finding the inverse z transform of the given signal. Can anyone help me? I'd appreciate it. Thanks!

Here is basically what I did:

However, I don't know what to do next. What is the next thing to do? Thanks!

Been a while for me, but might look at:
starting with the original F(z), consider
z → z /3
Then look at the z transform for f[n] = [n²]
and finally realize z^-1F(z) ↔ f[n-1]u[n-1].