Are there any good approximations for Stirling numbers which are less computationally intensive? To be a bit more specific, assuming a particular parametrization of the generalized Stirling numbers:
$S(a,b;-1,-d,0)=\frac{1}{b!(-d)^b}\sum^{b}_{j=0}(-1)^{b-j}{b \choose j}\prod_{k=0}^{a-1}(k-jd)$
This is very computationally expensive. I know that we can replace all factorials/gammas using the Stirling approximation, but that only is a good asymptotic approximation. Any pointers, ideas, appreciated.