{"uid":"cap_DU4_zigx5GIO6l5AT7Nyl","slug":"numora-catalan-number-generator-67de42e3","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://numorapoi.orbonomy.xyz/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":"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":"$0.02/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_NzWng3XqvfB2wp5KDZhFx","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","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 for a given non-negative integer n","exampleAgentPrompt":"What is the 12th Catalan number? I need it for a combinatorics problem involving counting the number of valid bracket sequences.","exampleUseCases":null,"resultDescription":"Returns a JSON object with a boolean success flag, a result object containing the computed Catalan number for the given index n, and a human-readable computation string describing what was calculated.","failureModes":["Missing required field 'n' returns a 400 validation error","Non-integer or negative value for n may return an error or undefined result","Very large n may cause overflow or extremely slow computation","Payment not provided or invalid x402 micropayment returns 402 Payment Required","Server unreachable returns 5xx error"],"whenToPreferThis":"Use this endpoint when you need a precise, server-side computation of a Catalan number by index and want a zero-dependency pure math result without implementing the formula yourself. Ideal for combinatorics tasks, counting problems (polygon triangulations, Dyck paths, binary trees), or number theory workflows where Catalan numbers are needed on demand.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T00:46:13.238Z","isFirstParty":false}