Binomial coefficient (n choose k) equals (-1)^k ((k-n-1) choose k)

Theorem

The following formula holds: $${n \choose k} = (-1)^k { {k-n-1} \choose k},$$ where ${n \choose k}$ denotes the binomial coefficient.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 3.1.3