{"id":"integer-catalan-number","version":"1.0.0","description":"Compute the nth Catalan number exactly.","supported_operations":["integer catalan number","nth catalan number","catalan sequence"],"unsupported_operations":["negative index","binomial coefficient","motzkin numbers"],"semantics":["n is a JSON integer from 0 to 100000.","C(0) is 1. The sequence is computed via the exact integer recurrence C(i+1) = C(i) * 2*(2i+1) / (i+2), each step an exact division, never floating point.","Requests whose exact result would exceed 1000 digits are rejected rather than truncated."],"limits":{"max_n":100000,"max_digits":1000},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["n"],"properties":{"n":{"type":"integer","minimum":0,"maximum":100000}}},"output_schema":{"type":"object","additionalProperties":false,"required":["value"],"properties":{"value":{"type":"string"}}},"examples":[{"input":{"n":5},"output":{"value":"42"}}],"execute_url":"/v1/tools/integer-catalan-number/versions/1.0.0/execute"}