Ratazong answered your recursion question above. You're probably getting -1 because numbers in intermediate results are too big. If you're trying to calculate something like

  N! / (K! * (N-K)!)
= (N * (N-1) * ... * (K+1)) / ((N-K) * (N-K-1) * ... * 1)
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you need to either mix up the multiplications and divisions so the intermediate results stay near the magnitude of the final result, or operate in log-space:

= exp((log N + log (N-1) + ... + log (K+1)) - (log (N-K) + log (N-K-1)
+ + ... + 0))
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