Calculates the number of group combinations possible given a number n and a number of sets k.

stirling_and_bell.py

def stirling(n, k):
    if k > n:
        return 0
    elif k == n or k == 1:
        return 1
    else:
        return (k*stirling(n-1, k) + stirling(n-1, k-1))

def bell(n):
    bell = 0
    for sets in range(1, n+1):
        bell += stirling(n, sets) 
    return bell
    
# If we try to split into more groups than we have people - it is not possible. If k and n are equal there is only one way to do it

# The formula for calculating the Stirling numbers is
#  S(n, k) = k*S(n-1, k) + S(n-1, k-1)

# The Bell number B(n) is the number of ways of splitting n into any number of parts from 0 to n
# B(n) is the sum of S(n,k) for k =1,2, ... , n.