Calculate the frequencies of different total face values for rolling n six sided dice.

dice.py

#Naive version. Takes a couple of minutes for 11 dice on my laptop
#from itertools import product
#from collections import Counter
#
#dice = int(input('How many dice? '))
#result = Counter(map(sum, product(range(1, 7), repeat=dice)))
#print(result)

def choose(n, k):
    """
    A fast way to calculate binomial coefficients by Andrew Dalke (contrib).
    http://stackoverflow.com/a/3025547/500584
    """
    if 0 <= k <= n:
        ntok = 1
        ktok = 1
        for t in range(1, min(k, n - k) + 1):
            ntok *= n
            ktok *= t
            n -= 1
        return ntok // ktok
    else:
        return 0

def freq(sides, dice, amount):
    # http://digitalscholarship.unlv.edu/cgi/viewcontent.cgi?article=2852&context=thesesdissertations
    m = sides
    n = dice
    k = amount - dice
    total = 0
    for j in range(max(m, k)):
        term = (-1) ** j
        term *= choose(n, j)
        term *= choose(n - 1 + k - m * j, n - 1)
        total += term
    return total

sides = 6
dice = int(input('How many dice? '))
sums = range(dice, dice * sides + 1)
#freqs = [freq(sides, dice, amount) for amount in sums]
freqs = [freq(sides, dice, amount) for amount in sums[:(len(sums) + 1) // 2]]
if len(sums) % 2 == 1:
    freqs += freqs[-2::-1]
else:
    freqs += freqs[-1::-1]
    
result = dict(zip(sums, freqs))
print(result)

nice work