1.75 Given 20 points on a circle, and connect them with 10 chords that have no common endpoints and do not intersect each other, how many different ways of connecting are there?
［Solution］Let the total number of different ways to connect $2 n$ points on a circle with $n$ chords, such that no two chords intersect inside the circle, be $k_{n}$. Select a point $A$ from the given points and assume it is connected to point $B$ by a chord $A B$. Then, points $A$ and $B$ divide the circle into two arcs, each containing an even number of given points. Suppose the arc from $A$ to $B$ in the clockwise direction contains $2 j$ points, then the other arc contains $2(9-j)$ points. The number of different ways to connect the points in each arc are $k_{j}$ and $k_{9-j}$, respectively. Therefore, the number of different ways to connect the points with the chord $A B$ as one of the chords is $k_{j} \cdot k_{9-j}$. Thus, we obtain the following recurrence relation:
$$
k_{n}=k_{n-1}+k_{1} k_{n-2}+k_{2} k_{n-3}+\cdots+k_{n-2} k_{1}+k_{n-1}.
$$

It is easy to see that $k_{1}=1, k_{2}=2$. Using the above recurrence relation, we can sequentially calculate: $k_{3}=$ $5, k_{4}=14, k_{5}=42, k_{6}=132, k_{7}=429, k_{8}=1430, k_{9}=4862, k_{10}=$ 16796. Therefore, the total number of different ways to connect the points is 16796.