{"uid":"cap_lglyVO9ao13sdYu4GdZ2h","slug":"catalan-number-calculator-f22eb45d","name":"Catalan Number Calculator","description":"Calculate the nth Catalan number.","url":"https://sovereign-x402-zeta.vercel.app/api/v1/sequence/catalan?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method","bodyType","body"],"properties":{"body":{"type":"object","properties":{},"additionalProperties":true},"type":{"type":"string","const":"http"},"method":{"enum":["POST","PUT","PATCH"],"type":"string"},"bodyType":{"enum":["json","form-data","text"],"type":"string"}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object"}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.001","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.001/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.001","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.001","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_c5G0nlq5erbYikgVVsLkB","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.001","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the nth Catalan number given a non-negative integer index n","exampleAgentPrompt":"What is the 12th Catalan number?","exampleUseCases":[{"title":"Combinatorics homework helper","prompt":"I need to know the Catalan number for n=8 — can you compute that for me?"},{"title":"Triangulation count for polygon","prompt":"How many ways can a convex polygon with 10 sides be triangulated? Compute the corresponding Catalan number at position 8."},{"title":"Valid bracket sequence counter","prompt":"What is the number of valid ways to arrange 6 pairs of parentheses? That's the 6th Catalan number — can you calculate it?"}],"resultDescription":"Returns the nth Catalan number as an integer value for the given index n, representing the count of various combinatorial structures such as valid bracket arrangements, binary tree shapes, or polygon triangulations.","failureModes":["Missing or invalid 'n' input returns an error","Non-integer or negative index may return a validation error","Very large n values may cause computation overflow or timeout","Malformed request body returns a 400-level error","Payment failure or insufficient USDC balance prevents execution"],"whenToPreferThis":"Choose this endpoint when you need a quick, on-demand computation of a specific Catalan number without setting up a local math library. It is ideal for agents handling combinatorics queries, educational tools, or applications that occasionally need Catalan numbers without wanting to implement the formula themselves.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-13T12:33:04.909Z","isFirstParty":false,"canonicalSlug":"catalan-number-calculator-f22eb45d"}