{"uid":"cap_dCUMUr8xExbsK-FSMEmol","slug":"numora-catalan-number-generator-201cc44f","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://numormo.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_ag8t5jrklL6EeARKAkO1L","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 given an integer index n","exampleAgentPrompt":"What is the 12th Catalan number? I need it for a combinatorics problem involving valid bracket sequences.","exampleUseCases":[{"title":"Counting valid bracket sequences","prompt":"How many valid ways can I arrange 7 pairs of parentheses? Compute the 7th Catalan number for me."},{"title":"BST structure enumeration","prompt":"I'm working on a data structures problem — how many structurally unique binary search trees can be formed with 9 nodes? That's the 9th Catalan number."},{"title":"Polygon triangulation counting","prompt":"For a convex polygon with 11 vertices, how many distinct triangulations exist? Can you calculate the Catalan number for n=9 to figure this out?"}],"resultDescription":"Returns a JSON object with success: true, a result object containing the computed Catalan number value for the given index n, and a computation string describing in human-readable terms what was calculated (e.g. 'The 10th Catalan number is 16796').","failureModes":["Missing required parameter n returns a validation error","Non-integer or negative n may return an error or undefined behavior","Very large n may cause integer overflow or timeout","Payment failure via x402 returns a 402 Payment Required response before computation occurs"],"whenToPreferThis":"Use this endpoint when you need a precise, server-side computation of Catalan numbers without implementing the algorithm yourself, especially in agent pipelines that require verified math results for combinatorics, dynamic programming, or sequence analysis. Prefer it over LLM-generated math when exactness matters, and over general-purpose compute services when you want a lightweight, single-purpose math API with per-call micropayment pricing.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T19:06:38.463Z","isFirstParty":false}