import matplotlib.pyplot as plt

def explicitFact(n):
    if(n <= 1):
        return 1
    out=1
    for k in range(2,n+1):
        out *= k
    return out

factsArray = [1,1]
def fact(n):
    if(n >= len(factsArray)):
        for k in range(len(factsArray),n+10):
            factsArray.append(factsArray[-1] * k)
    return factsArray[n]

def choose(n,k):
    return (fact(n) // (fact(k) * fact(n-k)))

def bwerk(b,n):
    return (choose(n,b+1) - choose(n-b-1, b+1) - (b+1) * choose(n-b-1,b) - 1) /\
        ((16**b) * (n**(b+1)))

def plotAtB(b):
    r = range(b**b, b**b+142)
    plt.plot(r, [ bwerk(b,n) for n in r])
    plt.show()