# Numora Catalan Number Generator

> Numora Catalan Number Generator is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.02/call, status unknown (last checked 2026-09-16).

Computes the nth Catalan number — a combinatorial sequence used in counting nested structures, bracket expressions, and tree topologies.

## Facts

- Endpoint: POST https://numomo.vercel.app/api/generate/catalan
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-16
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-catalan-number-generator-52bf8946
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_7rE8uNSQh_JpILNj7zoOu

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-52bf8946 -d '<json body>'
```

Example prompt: 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.

## When to prefer this

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.

## Known failure modes

- 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

## 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 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.

## 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-52bf8946/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)