Work out catalan number instantly with clear inputs, formula shown and shareable results.
The Catalan numbers Cₙ = C(2n, n)/(n + 1) count balanced bracket strings, binary trees with n internal nodes, triangulations of a convex polygon and monotonic lattice paths staying below the diagonal.
Catalan number
Cₙ = C(2n, n) / (n + 1) = (2n)! / (n!(n+1)!)
C(16, 8)/9 = 12870/9 = 1430.
They all reduce to the same recursive splitting structure Cₙ₊₁ = ΣCₖCₙ₋ₖ, which uniquely determines the sequence.