The Catalan recurrence C(n)=∑k=1n−1C(k)⋅C(n−k)C(n) = \sum_{k=1}^{n-1} C(k) \cdot C(n-k)C(n)=∑k=1n−1C(k)⋅C(n−k) with C(1)=1C(1)=1C(1)=1 counts which objects?
Permutations of nnn elements
Full binary trees with nnn leaves
Fibonacci sequences
All subsets of nnn elements