Z-transform of 1/n^2

I am trying to find the Z-transform of the sequence 1/n^2 (n >= 1).
I'd appreciate if anyone can tell me what the closed-form expression is
(assuming it has one) and/or give a suitable reference. I think the
region of convergence is |z| >= 1. If we consider the two-sided
sequence 1/n^2 (defined to be zero for n=0), the RoC would be |z| = 1.
Thanks.

vv

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