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Catalan numbers in java
The nth Catalan number in terms of binomial coefficients is calculated by the formula
(n + k )/k where k varies from 2 to n and n ≥ 0. i.e.
Cn = (2n)!/((n+1)!n!)
Program
public class CatalanNumbers {
public static long fact(int i) {
if(i <= 1) {
return 1;
}
return i * fact(i - 1);
}
public static void main(String args[]) {
Scanner sc = new Scanner(System.in);
System.out.println("Enter a number :");
int num = sc.nextInt();
//(2n)!/(n+1)!*n!
for(int i = 0; i<=num; i++) {
long Cn = (fact(2*i))/(fact(i+1)*fact(i));
System.out.println("C"+i+": "+Cn);
}
}
}
Output
Enter a number : 7 C0: 1 C1: 1 C2: 2 C3: 5 C4: 14 C5: 42 C6: 132 C7: 429
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