calculating n choose n/2 overflow

general
, ,
1

For the SPOONS problem I pre computed an array of values n choose floor(n/2).However I’m getting overflow as i noticed negative numbers after some n = 20 .I have used unsigned long long datatype,shoudn’t it be enough for numbers till 10^18?? Perhaps my multiplication of ints or something must be the problem.
Heres my code(i.e. the exact function:

void precompute(ull choose[65])
{
int r = 0;         // ull is unsigned long long
bool alt = 1;
choose[1] = 1;
for ( int n =  2 ; n < 65 ; ++n)
{
 if (alt)
    {
        r += 1;
        choose[n] =  choose[n-1]   * (n /  r);  // am calculating n choose [n/2]
        alt = 0;
    }
 else {
    choose[n] = choose[n-1] / (n -r)  * (n);
    alt = 1;
        }
 } 
 }

whats the problem ??