Narayana Numbers

The value of $N(0)$ is 1 because there is only one way to arrange 0 pairs of parentheses.

The value of $N(1)$ is 1 because there is only one way to arrange 1 pair of parentheses.

The value of $N(2)$ is 2 because there are two ways to arrange 2 pairs of parentheses: $((()))$ and $(())()$.

The value of $N(3)$ is 5 because there are five ways to arrange 3 pairs of parentheses: $(((()))), ((())()), (())(()), (()())(),$ and $(()())()$.

The value of $N(4)$ is 14 because there are 14 ways to arrange 4 pairs of parentheses.

The value of $N(5)$ is 42 because there are 42 ways to arrange 5 pairs of parentheses.

The value of $N(6)$ is 132 because there are 132 ways to arrange 6 pairs of parentheses.

The value of $N(7)$ is 429 because there are 429 ways to arrange 7 pairs of parentheses.

The value of $N(8)$ is 1430 because there are 1430 ways to arrange 8 pairs of parentheses.

The value of $N(9)$ is 4862 because there are 4862 ways to arrange 9 pairs of parentheses.

The value of $N(10)$ is 16796 because there are 16796 ways to arrange 10 pairs of parentheses.

The value of $N(11)$ is 58786 because there are 58786 ways to arrange 11 pairs of parentheses.

The value of $N(12)$ is 208012 because there are 208012 ways to arrange 12 pairs of parentheses.

The value of $N(13)$ is 742900 because there are 742900 ways to arrange 13 pairs of parentheses.

The value of $N(14)$ is 2674440 because there are 2674440 ways to arrange 14 pairs of parentheses.