# Numora Catalan Number Generator

> Numora Catalan Number Generator is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.02/call, status unknown (last checked 2026-09-15).

Computes the nth Catalan number for a given non-negative integer n

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/generate/catalan
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-catalan-number-generator-67de42e3
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_DU4_zigx5GIO6l5AT7Nyl

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-67de42e3 -d '<json body>'
```

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

## When to prefer this

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.

## Known failure modes

- 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

## 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 flag, 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-67de42e3/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)