Definition:Binomial Coefficient/Historical Note
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The binomial coefficients have been known about since at least the ancient Greeks and Romans, who were familiar with them for small values of $k$.
See the historical note to Pascal's Triangle for further history.
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.6$: Binomial Coefficients