homework and exercises - Canonical partition of a boson gas

I have a 1D gas made of $N$ particles placed in a harmonic potential well, so the Hamiltonian is:

$$ \mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right )$$

The first part of the exercise asked me to find the canonical partition at temperature $T$ if the particles are distinguishable, then to find the partition if the particles are indistinguishable, but the Maxwell-Boltzmann approximation applies. In both cases this was easy. But now the exercise asks me to find the partition if the particles are identical bosons, and then to show that this is equal to the Maxwell-Boltzmann approximation for large temperatures.

I don't know exactly how to set up the summation to count the states properly when you treat them as bosons. I know we have the states $\epsilon_j = \hbar \omega (j+\tfrac{1}{2})$ and that each of those states will be occupied by $n_j$ bosons and since it's 1D I don't have to worry about degeneracy...but I'm unsure how to continue.

From what I understand, it's nicer to work with fermions and boson in the grand canonical ensemble, but we haven't seen this in class yet.

Thanks!