The Catalan Calculator

Counting Structur

Catalan numbers ($C_n$) appear in many counting problems, like "how many ways can we arrange $N$ pairs of parentheses?" Formula: $C_n = rac{1}{n+1} inom{2n}{n}$ or via the iterative product: $prod_{i=1}^n rac{n+i}{i}$.

The Assignment

Your function receives a parameter n.

1. Initialize catalan to 1.
2. Use a loop from 1 to n.
3. In each step, calculate: catalan = catalan * (n + i) / i.
4. Finally, divide by (n + 1) (though using the product formula $prod rac{n+k}{k}$ is often cleaner).
5. Print the integer result (Math.round).