C++でパスカルの三角形を計算する

計算する段数を入力(２０まで) num = 20
1,
1,1,
1,2,1,
1,3,3,1,
1,4,6,4,1,
1,5,10,10,5,1,
1,6,15,20,15,6,1,
1,7,21,35,35,21,7,1,
1,8,28,56,70,56,28,8,1,
1,9,36,84,126,126,84,36,9,1,
1,10,45,120,210,252,210,120,45,10,1,
1,11,55,165,330,462,462,330,165,55,11,1,
1,12,66,220,495,792,924,792,495,220,66,12,1,
1,13,78,286,715,1287,1716,1716,1287,715,286,78,13,1,
1,14,91,364,1001,2002,3003,3432,3003,2002,1001,364,91,14,1,
1,15,105,455,1365,3003,5005,6435,6435,5005,3003,1365,455,105,15,1,
1,16,120,560,1820,4368,8008,11440,12870,11440,8008,4368,1820,560,120,16,1,
1,17,136,680,2380,6188,12376,19448,24310,24310,19448,12376,6188,2380,680,136,17,1,
1,18,153,816,3060,8568,18564,31824,43758,48620,43758,31824,18564,8568,3060,816,153,18,1,
1,19,171,969,3876,11628,27132,50388,75582,92378,92378,75582,50388,27132,11628,3876,969,171,19,1,
1,20,190,1140,4845,15504,38760,77520,125970,167960,184756,167960,125970,77520,38760,15504,4845,1140,190,20,1,

#include <iostream>
uint64_t nCr(int, int);
uint64_t factorial(int n);
int main() {
    
    int num;

    do{
        std::cout << "計算する段数を入力(２０まで) num = ";
        std::cin >> num;
    } while (num > 20);

    for (int i = 0; i <= num; i++) {
        for (int j = 0; j <= i; j++) {
            std::cout << nCr(i, j) << ",";
        }
        std::cout << std::endl;
    }
    return 0;
}
uint64_t nCr(int n, int r) {
    return factorial(n) / (factorial(r) * factorial(n - r));
}
uint64_t factorial(int n) {
    uint64_t result = 1;
    while (n > 1) {
        result *= n;
        n--;
    }
    return result;
}