#! /usr/bin/env python
"""
 Module MyStuff is a collection of useful functions which are 
 user defined, stored locally at $HOME/python/mymodules/mystuff.py
 where the mymodules directory has been added to the $PYTHONPATH  
 environment.


 Symbols:
 
  'm' is positive integer
  'n' is a positive integet such that n >= m >= 0


Paul Eugenio
Florida State University
Department of Physics
Jan 2019
"""

from __future__ import division, print_function
import sys
from math import factorial


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


def lobb_number(m, n):
    """  
    Lobb numbers form a natural generalization of the Catalan numbers,    
    Catalan recursive function defined via integer arithmetic 

    Lobb numbers L_n,n = 1 & Lobb_),n = 1/(1+n) Bionomial(2n, n)
    """
    return binomial(2*n, m+n )* (2*m+1) // (m+n+1)



def test_functions():
    """
    Routines to test module functions.  To execute test of function run 
    module as python program along with commandline argument "test"
        example: "mypython test" 
    """
    # test catalan function
    if( lobb_number(1, 3) == 9 ):
        print("Module is Good")
    else:
        print("WARNING!!!\n catalan() function failed test\n DO NOT USE!!!")

  
#
# main
#

if __name__ == '__main__':
    # the test block
    if len(sys.argv) == 2 and sys.argv[1] == 'test':
        test_functions()