A mathematical Facebook group posted a picture with the following claimed identity:
$$ \sum_{n=0}^{\infty} \frac{1+14 n+76 n^{2}+168 n^{3}}{2^{20 n}}\binom{2n}{n}^{7}=\frac{32}{\pi^{3}}. $$
they didn't provide any source for this claim, but it appears that it might be a conjecture.
Is this a familiar series? If so, what are its origins?