Integer derangements count

integer-derangements-count · version 1.0.0 · Numbers & math · free, no key needed

Compute !n, the number of derangements (permutations with no fixed point) of n items, exactly.

Use when you need to: integer derangements count · subfactorial · permutations with no fixed points.

Supported

• integer derangements count
• subfactorial
• permutations with no fixed points

Not supported

• negative index
• partial derangements
• floating-point approximation

Behavior

• n is a JSON integer from 0 to 100000.
• !0 is 1 (the empty permutation) and !1 is 0 (a single item cannot avoid its own position).
• The sequence is computed via the exact integer recurrence !n = (n-1) * (!(n-1) + !(n-2)), 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": 4
}

Response:

{
  "result": {
    "value": "9"
  }
}

How to call it

MCP

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

{
  "id": "integer-derangements-count",
  "version": "1.0.0",
  "input": {
    "n": 4
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/integer-derangements-count/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"n":4}'

The machine-readable contract is at /v1/tools/integer-derangements-count/versions/1.0.0.

CLI

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

Get the client at /clients/cli/.

Related tools

• Integer permutations count: Compute the exact number of k-permutations of n distinct items, P(n, k) = n! / (n-k)!.
• Integer binomial coefficient: Compute the exact binomial coefficient C(n, k), the number of ways to choose k items from n.
• Integer divmod: Integer quotient and remainder truncated toward zero.
• Integer totient: Compute Euler's totient function: the count of integers in [1, value] coprime to value.
• Array integer adjacent diff: Replace an array of canonical integer strings with consecutive first differences.
• Array integer clamp: Clamp an array of canonical integer strings to optional inclusive min and max bounds.