# Java: Print out the first 10 Catalan numbers by extracting them from Pascal's triangle

## Java Numbers: Exercise-8 with Solution

Write a Java program to print out the first 10 Catalan numbers by extracting them from Pascal's triangle.

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the Belgian mathematician Eugène Charles Catalan.

The first Catalan numbers for n = 0, 1, 2, 3, … are 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452,

**Sample Solution:**

**Java Code:**

```
import java.util.Scanner;
public class Example8 {
public static void main(String[] args) {
int num = 10;
int[] t = new int[num + 2];
t[1] = 1;
System.out.printf("\nList 10 Catalan numbers:-\n");
for (int i = 1; i <= num; i++) {
for (int j = i; j > 1; j--)
t[j] = t[j] + t[j - 1];
t[i + 1] = t[i];
for (int j = i + 1; j > 1; j--)
t[j] = t[j] + t[j - 1];
System.out.printf("\n%d ", t[i + 1] - t[i]);
}
System.out.printf("\n");
}
}
```

Sample Output:

List 10 Catalan numbers:- 1 2 5 14 42 132 429 1430 4862 16796

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