Counting the number of valid bracket permutations for a given length

Example:
Input: 3
Output: 5
Explanation: The following permutations are valid:
((())),(())(),()(()),(()()),()()()
The following permutations are invalid:
)()()(,())(() etc.
Program:
#include<iostream>
#include<string.h>
#include<stdio.h>
using namespace std;
int main()
{
 int fun(char[],int,int,int);
 int n;
 cin>>n;
 char A[100]="";
 cout<<fun(A,0,0,n)<<endl;
}
int fun(char A[],int open,int close,int n)
{
 static int count=0;
 if(open-close<0 || open-close>n || open>n)
 {
  return count;
 }
 else if(strlen(A)==2*n)
 {
  //cout<<A<<endl;
  count++;
  //cout<<count<<" "<<endl;
  return count;
 }
 else
 {
  A[strlen(A)]='(';
  A[strlen(A)+1]=0;
  fun(A,open+1,close,n);
  A[strlen(A)-1]=0;
  A[strlen(A)]=')';
  A[strlen(A)+1]=0;
  fun(A,open,close+1,n);
  A[strlen(A)-1]=0;
  return count;
 }
}
Sample Input: 15
Sample Output: 9694845