ScorpTech x402 API

Central Binomial

central_binomial

Read-onlyIdempotent

The nth central binomial coefficient (2n)!/(n!)^2. C(0) is 1, C(1) is 2, C(5) is 252, and C(10) is 184756. n runs from 0 to 200. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/central-binomial

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "n": "<n>"
    },
    "name": "central_binomial"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.5/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Beyond the annotations, the description details a critical output behavior: values past 15 digits will be returned as a decimal string. It also provides operational transparency regarding price and specific API endpoints/methods.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

While it is a dense block of text, it front-loads the mathematical definition and constraints before adding operational metadata (cost, URL). It manages to pack a lot of necessary information into a single concise passage.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a specialized mathematical tool, the description is highly complete, covering the definition, the valid domain of the input, the format of the output (decimal string for large numbers), and operational logistics (cost).

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Since schema description coverage is 0%, the description must compensate. It explicitly states the operational boundaries for the input parameter 'n', specifying that it runs from 0 to 200, which is vital for correct usage.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly identifies the mathematical function (nth central binomial coefficient) and provides specific examples (C(0)=1, C(5)=252), making it unambiguous.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

It provides explicit operational constraints, such as the range of 'n' (0 to 200) and the financial cost of the tool. It implies its use is specific to this combinatorial function rather than a generic calculation.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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