Find the radius of convergence of the series given-complex analysis

Find the radius of convergence of the series given

a) Σ(n=0 to ∞) [((a_{n})^n) z^(n^2)]

b) Σ(n=0 to ∞) [a_{n}) z^(n^2)]
Thanks for your help

a) Using the Root Test, we have
r = lim sup |(a(n))^n z^(n^2)|^(1/n)
..= lim sup |a(n)| * |z|^n.

For convergence, we need lim sup |a(n)| * |z|^n < 1.

b) Using the Root Test, we have
r = lim sup |a(n z^(n^2)|^(1/n)
..= lim sup |a(n)|^(1/n) * |z|^n.

For convergence, we need lim sup |a(n)|^(1/n) * |z|^n < 1.

**Is there some other piece of information that should be in this question?