Creating pascal triangle using 1-Dimensional array for finding coefficients of (1+x)^n efficiently.

Hi friends,
     As you all know pascal triangle looks like
                                                                     1                                      n=0
                                                                 1      1                                  n=1
                                                             1      2      1                              n=2
                                                          1     3       3      1                         n=3
                                                       1     4     6      4      1                      n=4
                                                    1     5    10   10     5     1                   n=5
                                                 ............................................                so on
Observe some facts:
1)Number of element in ith row = (i+1)

2) ith element in nth row = sum of (i-1)th & (i)th element in (n-1)th row  for 1<i<(n+1)

3)Also ,
For n=0:     (1+x)^0=1
For n=1:     (1+x)^1=1 + 1*(x)
For n=2:     (1+x)^2=1 + 2*(x) + 1*(x*x)
For n=3:     (1+x)^3=1 + 3*(x) + 3*(x*x) + 1*(x*x*x)

Observe the coefficients underlined, they belongs to each row of above triangle. For eg. when n=2,
coefficients are (1,2,1) which is row number 2 of pascal triangle. Similar situation occurs for n=3,here
coefficients are (1,3,3,1) which is row number 3 of pascal triangle.

4)Coefficients of (1+x)^n form sequence :      (nC0,nC1,nC2,.....nCn)    
where nCr=(n!)/(r! * (n-r)!)

So,by finding nth row of pascal triangle we are finding coefficients of (1+x)^n and hence indirectly above sequence of combinations.

Now we will see how to generate above pascal triangle recursively for specified value of 'n' using 1-D array in c++.

Size of 1-D array for above triangle for some n = 1+2+3+....+(n+1) =
 ((n+1)*(n+2))/2

Starting index in this 1-D array for nth row of  pascal triangle= 1+2+...n =
(n*(n+1))/2

//Actual c++ routine starts here:

void Form_Pascal_Triangle(unsigned long int a[],unsigned long int n)
{
    if(n==0)
    {
        a[0]=1;
    }
    else
    {
        Form_Pascal_Triangle(a,n-1);

        unsigned long int PREVTO_NTH_ROW_START_INDEX=(n*(n-1))/2;

        unsigned long int CURRENT_NTH_ROW_START_INDEX=(n*(n+1))/2;

        //initialise first and last element of nth row of pascal triangle
        a[CURRENT_NTH_ROW_START_INDEX]=1;
        a[CURRENT_NTH_ROW_START_INDEX+n]=1;

        for(unsigned long int i=1;i<n;i++)
        {
             a[CURRENT_NTH_ROW_START_INDEX+i] =
                                       a[PREVTO_NTH_ROW_START_INDEX+i-1] +
                                       a[PREVTO_NTH_ROW_START_INDEX+i];
        }
    }
}


int main()
{
    unsigned long int n;
    cout<<"Enter n:";
    cin>>n;
    unsigned long int size=((n*(n+1))/2)+(n+1);
    unsigned long int a[size];
 
    Form_Pascal_Triangle(a,n);

    return 0;
}

Please comment if any doubt and like if helpful.Thanks