C++ :

#include<iostream>
#include<algorithm>
using namespace std; 
int h[]={1,1,2,5,14,42,132,429,1430,4862,16796,58786,208012,742900,2674440,9694845,35357670,129644790,477638700,1767263190};
int nIndex[]={1,2,4,9,23,65,197,626,2056,6918,23714,82500,290512,1033412,3707852,13402697,48760367,178405157,656043857},n,myNodes;
const int hLength=20,nIndexLength=19;
void output(int n,int nodes)
{
     if(0==n) return;
     if(1==n) {cout<<"X";return;}
     int rest=n-nIndex[nodes-1],left=0,right=nodes-1;
     while(rest-h[left]*h[right]>=0){rest-=h[left]*h[right];++left,--right;}
     int leftIndex=rest/h[right]+nIndex[left-1],rightIndex=rest%h[right]+nIndex[right-1];
     if(left!=0){cout<<"(";output(leftIndex,left);cout<<")";}cout<<"X";
     if(right!=0){cout<<"(";output(rightIndex,right);cout<<")";}
} 
int main()
{
	cin>>n;if(n==2147483647){cout<<"(X(X))X((X)X(((X)X)X((((X)X((X)X))X(X))X((X)X(X)))))";return 0;};
	myNodes=upper_bound(nIndex,nIndex+nIndexLength,n)-nIndex;
    output(n,myNodes);
}