# Catalan Number Calculator

> Catalan Number Calculator is a paid API for AI agents from sovereign-x402-zeta.vercel.app, paid per call via x402, $0.001/call, status unknown (last checked 2026-10-13).

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

## Facts

- Endpoint: POST https://sovereign-x402-zeta.vercel.app/api/v1/sequence/catalan?utm_source=zero.xyz
- Price: $0.001/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-13
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/catalan-number-calculator-f22eb45d
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_lglyVO9ao13sdYu4GdZ2h

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 catalan-number-calculator-f22eb45d -d '<json body>'
```

Example prompt: What is the 12th Catalan number?

## When to prefer this

Choose this endpoint when you need a quick, on-demand computation of a specific Catalan number without setting up a local math library. It is ideal for agents handling combinatorics queries, educational tools, or applications that occasionally need Catalan numbers without wanting to implement the formula themselves.

## Known failure modes

- Missing or invalid 'n' input returns an error
- Non-integer or negative index may return a validation error
- Very large n values may cause computation overflow or timeout
- Malformed request body returns a 400-level error
- Payment failure or insufficient USDC balance prevents execution

## How this service works

Calculate the nth Catalan number.

## Output

Returns the nth Catalan number as an integer value for the given index n, representing the count of various combinatorial structures such as valid bracket arrangements, binary tree shapes, or polygon triangulations.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method",
    "bodyType",
    "body"
   ],
   "properties": {
    "body": {
     "type": "object",
     "properties": {},
     "additionalProperties": true
    },
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "POST",
      "PUT",
      "PATCH"
     ],
     "type": "string"
    },
    "bodyType": {
     "enum": [
      "json",
      "form-data",
      "text"
     ],
     "type": "string"
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object"
    }
   }
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/catalan-number-calculator-f22eb45d/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from sovereign-x402-zeta.vercel.app](https://www.zero.xyz/host/sovereign-x402-zeta.vercel.app/llms.txt)