Solve the recurrence relation: $I_p=\sigma^2(p-1)I_{p-2}+\mu I_{p-1}$

Question

$$ I_p=\sigma^2(p-1)I_{p-2}+\mu I_{p-1} $$ Does $I$ have a close form expression?

This is the recurrence relation satisfied by the $k$-the original moment of a folded normal distribution. See Here.

I don't know what to do because $p$ appears in the recurrence.