DECLARE FUNCTION factorial! (n AS INTEGER)
DECLARE FUNCTION binomial! (n AS INTEGER, k AS INTEGER)

DIM n AS INTEGER, k AS INTEGER

FOR n = 0 TO 14
    FOR k = 0 TO n
        PRINT USING " ####"; binomial(n, k);
    NEXT k
    PRINT
NEXT n
END

FUNCTION binomial! (n AS INTEGER, k AS INTEGER)
    ' Special cases
    IF k = 0 OR k = n THEN binomial = 1
    IF k < 0 OR k > n THEN binomial = 0

    ' For efficiency, we use the smallest value of k or (n-k)
    DIM tmp AS INTEGER
    tmp = k
    IF tmp > n - tmp THEN tmp = n - tmp

    DIM product AS DOUBLE ' Double to avoid overflow
    product = 1

    FOR i = 1 TO tmp
        product = product * (n - tmp + i) / i
    NEXT i

    binomial = product
END FUNCTION

FUNCTION factorial (n AS INTEGER)
    IF n <= 1 THEN factorial = 1

    DIM product AS DOUBLE ' Double to avoid overflow
    product = 1

    FOR i = 2 TO n
        product = product * i
    NEXT i

    factorial = product
END FUNCTION