fork download
copy 
  1. from itertools import product
  2. from operator import mul
  3.  
  4. def fact(x, ans=1):
  5.     if x<2: return ans
  6.     else: return fact(x-1, x*ans)
  7.  
  8. def choose(n, m):
  9.     return fact(n)/(fact(m)*fact(n-m))
  10.  
  11. def foo(n,m):
  12.     ans = 0
  13.     fact_m = fact(m)
  14.  
  15.     for num in product(range(m+1), repeat=n):
  16.         if sum(num) == m:
  17.             prod = fact_m
  18.             for x in num:
  19.                 if x>0:
  20.                     prod = prod * x**(x-1) / fact(x) #cannot be '*=' here!
  21.             ans += prod
  22.  
  23.     return ans * fact(n-1) * choose(n+m, n)
  24.  
  25. for n in range(1,7):
  26.     print '%d:'%n,
  27.     print '\t'.join(str(foo(n,m)) for m in range(1,9))
  28.  
  29. '''
  30. 1: 2    6	36	320	3750	54432	941192	18874368
  31. 2: 6	36	300	3360	47250	798336	15731352	353894400
  32. 3: 24	240	2760	38640	646800	12628224	281781360	7071989760
  33. 4: 120	1800	27720	480480	9510480	213373440	5365206000	149582315520
  34. 5: 720	15120	302400	6410880	149052960	3824029440	107915734080	3330566553600
  35. 6: 5040	141120	3568320	91324800	2476504800	72313274880	2282004204480	77725396869120
  36. '''
  37.  
  38. print '(SO)n=1:',
  39. print '\t'.join(str(i**(i-1)*(i+1))
  40.                 for i in range(1, 9))
  41.  
  42. print '(SO)n=2:',
  43. print '\t'.join(str(i**(i-2)*(2*i-1)*(i+1)*(i+2))
  44.                 for i in range(1,9))
  45.  
  46. print '(SO)n=3:',
  47. print '\t'.join(str(i**(i-3)*(4*i*i-5*i+2)*(i+1)*(i+2)*(i+3))
  48.                 for i in range(1,9))
  49.  
  50. print '(SO)n=4:',
  51. print '\t'.join(str(i**(i-4)*(4*i-3)*(2*i*i-3*i+2)*(i+1)*(i+2)*(i+3)*(i+4))
  52.                 for i in range(1,9))
  53.  
  54. '''
  55. (SO)n=1: 2	6	36	320	3750	54432	941192	18874368
  56. (SO)n=2: 6.0	36	300	3360	47250	798336	15731352	353894400
  57. (SO)n=3: 24.0	240.0	2760	38640	646800	12628224	281781360	7071989760
  58. (SO)n=4: 120.0	1800.0	27720.0	480480	9510480	213373440	5365206000	149582315520
  59. '''
  60.  
Success #stdin #stdout 0.52s 10840KB
comments (?)
stdin
copy 
Standard input is empty
stdout
copy 
1: 2	6	36	320	3750	54432	941192	18874368
2: 6	36	300	3360	47250	798336	15731352	353894400
3: 24	240	2760	38640	646800	12628224	281781360	7071989760
4: 120	1800	27720	480480	9510480	213373440	5365206000	149582315520
5: 720	15120	302400	6410880	149052960	3824029440	107915734080	3330566553600
6: 5040	141120	3568320	91324800	2476504800	72313274880	2282004204480	77725396869120
(SO)n=1: 2	6	36	320	3750	54432	941192	18874368
(SO)n=2: 6.0	36	300	3360	47250	798336	15731352	353894400
(SO)n=3: 24.0	240.0	2760	38640	646800	12628224	281781360	7071989760
(SO)n=4: 120.0	1800.0	27720.0	480480	9510480	213373440	5365206000	149582315520
https://ideone.com/lEoYGo
language:
Python (cpython 2.7.16)
created:
11 years ago
visibility:
secret

Share or Embed source code

Discover > Sphere Engine API

The brand new service which powers Ideone!

Discover > IDE Widget

Widget for compiling and running the source code in a web browser!