In case you’re fine with an approximation, you could try modelling the #P problem as a CNF (check this paper for more info) and use an approx model counter such as https://github.com/meelgroup/approxmc .
In case you’re fine with an approximation, you could try modelling the #P problem as a CNF (check this paper for more info) and use an approx model counter such as https://github.com/meelgroup/approxmc .