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  "body": "\n## Statement\n\nLet $n$ be a natural number.\nThen the number of [[Dyck words|0R9JR0465V]] of semilength $n$ is the [[Catalan number|092DRBFKMG]] $C_n$.\n\n## Remarks\n\nFor $n = 3$ the $5$ Dyck words are $UUUDDD$, $UUDUDD$, $UUDDUD$, $UDUUDD$ and $UDUDUD$.\nProof idea: a nonempty Dyck word has a unique form $U w_1 D w_2$, where $w_1$ and $w_2$ are Dyck words. This gives the [[Catalan recurrence|0Y1MG9R5VN]].\n\n## Explanations\n\n### L1 human\n\nEach nonempty balanced bracket string starts with an opening bracket, and that bracket has a matching closing bracket.\nThe inside and the part after the match are smaller balanced strings, so the count satisfies the Catalan recurrence.\n",
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