#!/usr/bin/env python
#--------------------------------------------------------------------
#	binomial.py
#
#	This program calls a recursively defined function to show 
#	some of the uppermost rows in the famous Pascal Triangle.
#
#		execute using:  $ python binomial.py
#
#	programmer: ALLAN CRUSE
#	written on: 27 JAN 2011
#--------------------------------------------------------------------

def binomial( n, k ):
	if ( n < 0 ) or ( k < 0 ) or ( n < k ):
		return 0
	else:
		if ( n == 0 ) or ( k == 0 ) or ( k == n ):
			return	1
		else:
			return	binomial( n-1, k-1 ) + binomial( n-1, k )


print
print "The top ten rows of Pascal's Triangle"
print
for n in range( 10 ):
	print "row #%-d: " % n,
	for k in range( n+1 ):
		print binomial( n, k ),
	print
print