#!/usr/bin/env python
#-*- coding: utf-8 -*-
from __future__ import division
import sys
MEMO = {}
def fact(n):
if ('f', n) in MEMO:
return MEMO[('f', n)]
if n > 0:
result = n * fact(n-1)
MEMO[('f', n)] = result
return result
else: return 1
def a(n):
from fractions import Fraction
ans = Fraction(0)
for k in xrange(0, n-1):
ans += Fraction(n**k, fact(k))
return fact(n-1) * ans
for i in xrange(2,19):
print i, a(i)
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