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.

Exact factorial n! for 0 ≤ n ≤ 20000, returned as a decimal string with its digit count.

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.

Number of ordered arrangements of r items from n, nPr = n!/(n-r)!. Requires r ≤ n and r ≤ 10000.