code: import java.util.HashMap;
  import java.util.Map;
  
  public class Catalan {
  	private static final Map<Long, Double> facts = new HashMap<Long, Double>();
  	private static final Map<Long, Double> catsI = new HashMap<Long, Double>();
  	private static final Map<Long, Double> catsR1 = new HashMap<Long, Double>();
  	private static final Map<Long, Double> catsR2 = new HashMap<Long, Double>();
  	
  	static{//pre-load the memoization maps with some answers
  		facts.put(0L, 1D);
  		facts.put(1L, 1D);
  		facts.put(2L, 2D);
  		
  		catsI.put(0L, 1D);
  		catsR1.put(0L, 1D);
  		catsR2.put(0L, 1D);
  	}
  
  	private static double fact(long n){
  		if(facts.containsKey(n)){
  			return facts.get(n);
  		}
  		double fact = 1;
  		for(long i = 2; i <= n; i++){
  			fact *= i; //could be further optimized, but it would probably be ugly
  		}
  		facts.put(n, fact);
  		return fact;
  	}
  
  	private static double catI(long n){
  		if(!catsI.containsKey(n)){
  			catsI.put(n, fact(2 * n)/(fact(n+1)*fact(n)));
  		}
  		return catsI.get(n);
  	}
  	
  	private static double catR1(long n){
  		if(catsR1.containsKey(n)){
  			return catsR1.get(n);
  		}
  		double sum = 0;
  		for(int i = 0; i < n; i++){
  			sum += catR1(i) * catR1(n - 1 - i);
  		}
  		catsR1.put(n, sum);
  		return sum;
  	}
  	
  	private static double catR2(long n){
  		if(!catsR2.containsKey(n)){
  			catsR2.put(n, ((2.0*(2*(n-1) + 1))/(n + 1)) * catR2(n-1));
  		}
  		return catsR2.get(n);
  	}
  	
  	public static void main(String[] args){
  		for(int i = 0; i <= 15; i++){
  			System.out.println(catI(i));
  			System.out.println(catR1(i));
  			System.out.println(catR2(i));
  		}
  	}
  }
  