combinatorics.openverbs.com publishes 3 machine-payable endpoints over the x402 protocol, priced from $0.004 to $0.004 per call. Each was probed directly; the response code below is what it returned.
| Endpoint | Method | Price | Probe |
|---|---|---|---|
| /v1/catalan | GET | $0.004 | 402 |
| /v1/combinations | GET | $0.004 | 402 |
| /v1/multinomial | GET | $0.004 | 402 |
The n-th Catalan number Cₙ = C(2n, n)/(n+1), counting balanced bracketings, binary trees, and many other structures. Requires n ≤ 10000.
Binomial coefficient nCr = n!/(r!(n-r)!), the number of unordered r-subsets of n. Requires r ≤ n and min(r, n-r) ≤ 10000.
Multinomial coefficient (k1+k2+…)! / (k1! k2! …) — the number of ways to partition n = Σki items into labelled groups of the given sizes. The sum must be ≤ 20000.