/**
 * This program demonstrates a triangular array.
 */
void main() {
    final int NMAX = 10;

    // allocate triangular array
    int[][] odds = new int[NMAX + 1][];
    for (int n = 0; n <= NMAX; n++)
        odds[n] = new int[n + 1];

    // fill triangular array
    for (int n = 0; n < odds.length; n++)
        for (int k = 0; k < odds[n].length; k++) {
            /*
             * compute binomial coefficient
             * n*(n-1)*(n-2)*...*(n-k+1)/(1*2*3*...*k)
             */
            int lotteryOdds = 1;
            for (int i = 1; i <= k; i++)
                lotteryOdds = lotteryOdds * (n - i + 1) / i;

            odds[n][k] = lotteryOdds;
        }

    // print triangular array
    for (int[] row : odds) {
        for (int odd : row)
            IO.print("%4d".formatted(odd));
        IO.println();
    }
}
