{"uid":"cap_7rE8uNSQh_JpILNj7zoOu","slug":"numora-catalan-number-generator-52bf8946","name":"Numora Catalan Number Generator","description":"100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.","url":"https://numomo.vercel.app/api/generate/catalan","method":"POST","headers":{},"bodySchema":{"type":"object","required":["n"],"properties":{"n":{"type":"integer"}}},"responseSchema":{"type":"object","required":["success","result","computation"],"properties":{"result":{"type":"object","description":"Computation result varies by endpoint"},"success":{"type":"boolean","description":"Always true on success"},"computation":{"type":"string","description":"Human-readable description of what was computed"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","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":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_lhkSNZ_BTPwr2XufcxcK4","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the nth Catalan number — a combinatorial sequence used in counting nested structures, bracket expressions, and tree topologies.","exampleAgentPrompt":"What is the 12th Catalan number? I need it for a combinatorics problem about the number of ways to fully parenthesize an expression with 13 factors.","exampleUseCases":[{"title":"Parenthesization count for expression","prompt":"How many distinct ways can I parenthesize a product of 8 factors? Use Catalan numbers with n=7 to figure that out."},{"title":"Counting binary tree topologies","prompt":"I'm working on a CS problem — how many full binary trees exist with 6 internal nodes? That should be the 6th Catalan number."},{"title":"Polygon triangulation count","prompt":"In how many ways can a convex polygon with 10 sides be triangulated? Calculate the Catalan number at index 8 for me."}],"resultDescription":"Returns a JSON object with a boolean 'success' field, a 'result' object containing the computed Catalan number for the given index n, and a human-readable 'computation' string describing what was calculated.","failureModes":["Non-integer or missing 'n' returns a validation error","Negative value of 'n' may return an error or undefined result","Very large values of 'n' may exceed integer precision or timeout","Payment failure via x402 prevents computation from proceeding"],"whenToPreferThis":"Choose this endpoint when you need an exact Catalan number for a specific index without setting up a local computation environment, especially inside an AI agent pipeline that benefits from zero-dependency pure math calls with micropayment access. Prefer it over general-purpose code execution when you want a deterministic, fast, self-contained API call.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-16T00:50:52.037Z","isFirstParty":false}