# Numora Catalan Number Generator

> Numora Catalan Number Generator is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.02/call, status unknown (last checked 2026-09-14).

Computes the nth Catalan number given an integer index n

## Facts

- Endpoint: POST https://numormo.vercel.app/api/generate/catalan
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-catalan-number-generator-201cc44f
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_dCUMUr8xExbsK-FSMEmol

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-catalan-number-generator-201cc44f -d '<json body>'
```

Example prompt: What is the 12th Catalan number? I need it for a combinatorics problem involving valid bracket sequences.

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

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.

## Output

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').

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "n"
 ],
 "properties": {
  "n": {
   "type": "integer"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "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"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-catalan-number-generator-201cc44f/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormo.vercel.app](https://www.zero.xyz/host/numormo.vercel.app/llms.txt)