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  "body": "\n## Proof\n\n1. Let $n$ be a natural number.\n2. The node [[Catalan numbers|092DRBFKMG]] defines the sequence $(C_m)$ by $C_0 = 1$ and, for every natural number $m$, $C_{m+1} = \\sum_{i=0}^{m} C_i\\, C_{m-i}$.\n3. Taking $m = n$ in this defining rule gives $C_{n+1} = \\sum_{i=0}^{n} C_i\\, C_{n-i}$, which is the claim.\n\n## Idea\n\nHere the Catalan numbers are defined by this recursion, so the recurrence is part of the definition. Its real content lies in the families that satisfy it, such as Dyck words and binary trees.\n",
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