#! /usr/bin/env python
"""
 pascal.py is program which calculates the binomial coefficient via
 a user defined function.  The program generates Pascal's triangle out to
 20 lines.

 In combinatorics of n elements disregarding their order, the binomial 
 coefficient (n,k) gives the number of ways to choose k elements (i.e. n choose k).
 Given 0 elements there is only the one way to chose 0 elements (0,0) =1
 Given 1 element there is 1 way to choose 0 elements (1,0) & 1 way to
 choose 1 element (1,1), ...  


 Paul Eugenio 
 PHZ4151C
 Jan 25, 2019
"""

# program header code
from __future__ import division, print_function
from math import factorial



def binomial(n, k):
    """ Binomial coefficient   (n k) = n!/(k!(n-k)! """
    return ( factorial(n) // (factorial(k)*factorial(n-k)) )


# constants
TRIANGLE_SIZE = 20


#
# main
#

# print out pascal's triangle
for n in range(TRIANGLE_SIZE):
    for k in range(0, n+1):
        print(binomial(n, k), end=' ')
    print(" ")