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Proposition: Recursive Formula for Binomial Coefficients
The binomial coefficient \(\binom nk\) can be for \(k,n\in\mathbb N\), \(n\ge 1\), \(n\ge k\) calculated using the following recursive formula:
\[\binom nk=\binom {n1}{k1} + \binom {n1}{k}.\]
We have the special cases
\(\binom n0=1\) for all \(n\in\mathbb N\) and
\(\binom nn=1\) for all \(n\in\mathbb N\).
Table of Contents
Proofs: 1
Mentioned in:
Parts: 1 2
Proofs: 3 4 5
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References
Bibliography
 Aigner, Martin: "Diskrete Mathematik", vieweg studium, 1993