Binomial coefficient identities (symmetry and Pascal) (C(n,r)=C(n,n−r); Pascal: C(n,r)=C(n−1,r−1)+C(n−1,r))
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C(n,r)=C(n,n−r); Pascal: C(n,r)=C(n−1,r−1)+C(n−1,r)
What each symbol means
| Symbol | What it stands for |
|---|---|
| n | Row index (non-negative integer) |
| r | Position in row |
| C(n,r) | Entries of Pascal’s triangle |
When to use this
Integers with 0 ≤ r ≤ n. Pascal’s recurrence needs r≥1 for C(n−1,r−1) term.