Cattleya number of combinatorial mathematics ---

 

 

Long  Long F [ 25 ];
 int main () { 
  F [ 0 ] = . 1 ; 
  CIN >> n-;
   for ( int I = . 1 ; I <= n-; I ++) F [I] = F [I - . 1 ] * ( . 4 * I - 2 ) / (I + . 1 );
   // here is the common formulas 2 
  COUT << F [n-] << endl;
   return  0 ; 
}

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The problem can be solved:
1. parentheses matching, n how many matching pair of parentheses way?

2. issue out of the stack, an infinite stack, 1,2,3 ... N How many different ways of pop

3. binary tree species problem: n nodes consisting of a binary tree, a total of how many different circumstances

4.n * n grid went to the upper right corner from the lower left, can not go diagonal, how many different moves

The method of seeking a convex polygon area into triangular areas: a convex polygon 5. The segmentation

6. The set partitioning problem: For the set {1,2,3, ... n} does not cross the divided number is the number

7. The product of restructuring: Matrix Chain P = a1 * a2 * a3 * ... an

8. Connection disjoint problems: methods of 2n points on a circle, and those points are connected together such that the n line segments obtained number of disjoint

9. queuing height: 2n different height of a person, each row must be in the order of high to low, the first and the second row of high parallelism, arranged to ask how many ways

10. Tickets find the money question:

11.