Number of partitions of $n$ with restrictions

Question

Find the ordinary generating function for the number of partitions of n in which all parts are odd and none surpasses 7. My answer is:

$$\prod\limits_{i=1}^7 \frac{1}{1-x^{2i}}$$

She is correct?

Answer 1

Hint: See this here. The generation function is $\large{\prod\limits_{i=1}^{\infty} \frac{1}{1-x^{2i-1}}}=\normalsize{\prod\limits_{i=1}^{\infty}}(1-x^i)$. For $n=7$ we get

$$\prod\limits_{i=1}^{7}(1-x^i)$$