Generalized Coupon Collector's problem

#!/usr/bin/env python

''' Expected numbers of coupons required to collect m sets of n coupons

    Using integral from p.23 of Ferrante & Saltalamacchia
    http://mat.uab.cat/matmat/PDFv2014/v2014n02.pdf
    Written by PM 2Ring 2015.09.05
'''

from __future__ import print_function, division

import sys
from mpmath import mp

#Set the precision
#mp.dps = 30

zero = mp.mpf(0)
one = mp.mpf(1)

#Factorial table
factorials = []

def make_func(n, m):
    fac = factorials[:m]
    def func(t):
        smt = sum(t**k / f for k,f in fac)
        return one - (one - smt * mp.exp(-t)) ** n
    return func

def main():
    #n: number of coupons; mm: max number of sets
    n = int(sys.argv[1]) if len(sys.argv) > 1 else 101
    n = mp.mpf(n)
    mm = int(sys.argv[2]) if len(sys.argv) > 2 else 10

    #Build factorial table
    factorials.append((zero, one))
    for i in range(1, mm):
        ii = mp.mpf(i)
        factorials.append((ii, ii * factorials[i-1][1]))

    print('Expected numbers of coupons required to collect m sets of %d coupons' % n)
    print(' m: expected number')
    for m in range(mm):
        v = n * mp.quad(make_func(n, m), [zero, mp.inf])
        print('%2d: %s' % (m, mp.nstr(v, 12)))


if __name__ == '__main__':
    main()