I think what he/she is looking for is the Poisson-Binomial distribution[1]. There is mention of one python package in the wikipedia article[2], but it doesn't seem to be widely used. There's an open issue from 2016 to implement it in scipy.stats[3].

[1] https://en.wikipedia.org/wiki/Poisson_binomial_distribution

[2] https://github.com/tsakim/poibin

[3] https://github.com/scipy/scipy/issues/6000