Quote Originally Posted by nuzzle View Post
Maybe the sum of binominals I have in my solution can be reduced to factorials but computationally it may be better to keep the binominals. It's because of the relationship with Pascal's triangle in this case. Factorials becomes awfully big very quickly and require lots of multiplications to compute. Binominals on the other hand stay smaller and if the recurrent Pascal's triangle algorithm is used only additions are needed. For example the factorial 20! is 2432902008176640000 while the binominal (20|10) is just 184756.

I looks like the OP is using Java and it sports a standard class for arbitrary-precision integers called BigInteger. Using BigInteger in combination with the very efficient recurrent Pascal's triangle algorithm would make it possible I think to find the exact solution to even something as big as f(100,50) in reasonable time.
I know what you mean but our purpose is to find a formula not a better way to calculate binomial
we can say in formula 50! and don't need to calculate it because it is formula