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### Coefficients of infinite polynomial products

I would first like to ask if there are commands for computing infinite products,

$$eg.\quad g=q \prod_{n=1}^{\infty} (1-q^{8n})(1-q^{16n}).$$

If not, are there commands for finite products then? Can I compute the above $K$ number of times?

Basically, I'm only interested in the coefficients of $g\theta_2$ and $g\theta_4$ where $g$ is as above and $\theta_t=\sum^{\infty}_{-\infty}q^{tn^2}$.

This link to OEIS seems to have a code for generating $g\theta_2$ in PARI, I always thought that SAGE is able to call pari, but I'm unable to perform the command on SAGE.

I'll appreciate it if anyone can advise me how best to do this or direct me to any resources, thanks!

### Coefficients of infinite polynomial products

I would first like to ask if there are commands for computing infinite products,

$$eg.\quad g=q \prod_{n=1}^{\infty} (1-q^{8n})(1-q^{16n}).$$

If not, are there commands for finite products then? Can I compute the above $K$ number of times? then?

Basically, I'm only interested in the coefficients of $g\theta_2$ and $g\theta_4$ where $g$ is as above and $\theta_t=\sum^{\infty}_{-\infty}q^{tn^2}$.

This link to OEIS seems to have a code for generating $g\theta_2$ in PARI, I always thought that SAGE is able to call pari, but I'm unable to perform the command on SAGE.

I'll appreciate it if anyone can advise me how best to do this or direct me to any resources, thanks!

### Coefficients of infinite polynomial products

I would first like to ask if there are commands for computing infinite products,

$$eg.\quad g=q \prod_{n=1}^{\infty} (1-q^{8n})(1-q^{16n}).$$

If not, are there commands for finite products then?then? How do you compute $$\quad g=q \prod_{n=1}^{N} (1-q^{8n})(1-q^{16n})?$$

Basically, I'm only interested in the coefficients of $g\theta_2$ and $g\theta_4$ where $g$ is as above and $\theta_t=\sum^{\infty}_{-\infty}q^{tn^2}$.

This link to OEIS seems to have a code for generating $g\theta_2$ in PARI, I always thought that SAGE is able to call pari, but I'm unable to perform the command on SAGE.

I'll appreciate it if anyone can advise me how best to do this or direct me to any resources, thanks!