bell_number.py

# Contribution by https://github.com/nightwarriorftw

#Python program to print bell number
#Bell Number:-Let S(n, k) be total number of partitions of n elements into k sets. The value of n’th Bell Number is sum of S(n, k) for k = 1 to n. Value of S(n, k) can be defined recursively as, S(n+1, k) = k*S(n, k) + S(n, k-1)
A sample Bell triangle is as follows:
1
1   3
3   8   13
13  23  33  43
#The code to print the bell triangle is as follows-
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
n=int(input("enter the number of bell"))     #taking value from the user
bell=0                                       #initialising bell to 'zero'
k=0                                          #initialising k to 'zero'
for i in range(0,n):                         #loop for changing rows from 0 to n
    for j in range(0,i+1):                   #printing columns
        if j==0 and i>0:                     #repeating the last number of previous row in new row
            print(bell,'',end='')            #printing first number of each line
        else:
            k=(i**2)+1+bell                  #to generate other numbers of line
            print(k,'',end='')               #printing other number in lines
            bell=k                           #updating value of bell 
    print('\n')                              #for moving into next lines           
print("last number of bell is",bell)