_03d_pascal_rec Namespace Reference

Pascal triangle using factorials. More...

Functions
def	factr (n)
	Factorial of n, recursive version. More...
def	fact (n)
	Factorial of n, non-recursive version. More...
def	kfact (n, k)
	k factorial of n. More...
def	pascal (n, k)
	The binomial coefficient, refered as row n, column k. More...
def	showpascal (n)
	Prints successive rows of Pascal's triangle, from 0 to n. More...

Detailed Description

Pascal triangle using factorials.

 0        1
 1       1 1
 2      1 2 1
 3     1 3 3 1
 4    1 4 6 4 1
 5  1 5 10 10 5 1

    0 1 2  3  4 5
 

Author

Paulo Roma

Since

12/04/2009

See also

http://en.wikipedia.org/wiki/Pascal_triangle

Function Documentation

fact()

def _03d_pascal_rec.fact

(

n

)

Factorial of n, non-recursive version.

The factorial, denoted by n!, is defined for a positive integer, and represents the product of all numbers less than or equal n.

Parameters

n	an integer.

Returns

n!

See also

https://docs.python.org/3/library/functools.html?highlight=reduce#functools.reduce

Referenced by factr(), and pascal().

factr()

def _03d_pascal_rec.factr

(

n

)

Factorial of n, recursive version.

The factorial, denoted by n!, is defined for a positive integer, and represents the product of all numbers less than or equal n.

Parameters

n	an integer.

Returns

n!

References fact().

kfact()

def _03d_pascal_rec.kfact	(		n,
			k
	)

k factorial of n.

Parameters

n	an integer.
k

Returns

n!/(n-k)!

Referenced by pascal().

pascal()

def _03d_pascal_rec.pascal	(		n,
			k
	)

The binomial coefficient, refered as row n, column k.

It also represents the number of combinations of n things taken k at a time (called n choose k).

Parameters

n	row.
k	column.

Returns

n!/(n-k)!k!

References fact(), and kfact().

Referenced by showpascal().

showpascal()

def _03d_pascal_rec.showpascal

(

n

)

Prints successive rows of Pascal's triangle, from 0 to n.

Parameters

n	a positive integer.

References _01d_dec2bin.input, and pascal().