Integer catalan number

integer-catalan-number · version 1.0.0 · Numbers & math · free, no key needed

Compute the nth Catalan number exactly.

Use when you need to: integer catalan number · nth catalan number · catalan sequence.

Supported

• integer catalan number
• nth catalan number
• catalan sequence

Not supported

• negative index
• binomial coefficient
• motzkin numbers

Behavior

• n is a JSON integer from 0 to 100000.
• C(0) is 1. The sequence is computed via the exact integer recurrence C(i+1) = C(i) * 2*(2i+1) / (i+2), each step an exact division, never floating point.
• Requests whose exact result would exceed 1000 digits are rejected rather than truncated.

Input

• n (integer, required): min 0; max 100000

Output

• value (string, required)

Limits

• max n: 100000
• max digits: 1000

Example

Request input:

{
  "n": 5
}

Response:

{
  "result": {
    "value": "42"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "integer-catalan-number",
  "version": "1.0.0",
  "input": {
    "n": 5
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/integer-catalan-number/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"n":5}'

The machine-readable contract is at /v1/tools/integer-catalan-number/versions/1.0.0.

CLI

node cli.mjs run integer-catalan-number 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

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