I'm reading about the Ramanujan tau function, defined in my lecture notes by
$q \prod_{n=1}^{\infty} (1-q^n)^{24} = \sum_{n=1}^{\infty} \tau(n) q^n$.
Wolfram provides the identity
$\tau(n) = \frac{65}{756}\sigma_{11}(n) + \frac{691}{756}\sigma_{5}(n) - \frac{691}{3} \sum_{k=1}^{n-1} \sigma_5 (k) \sigma_5 (n-k)$,
where $\sigma_k(n)$ is the divisor function, which it says has been found via the Cauchy product.
Unfortunately I have not seen this identity anywhere else, and I can't seem to see it worked through anywhere! I'd love to say I got anywhere trying it myself, but I am going to have to ask for help. Can anybody give me a hand??
Thanks in advance!