from itertools import product
from operator import mul
 
def fact(x, ans=1):
    if x<2: return ans
    else: return fact(x-1, x*ans)
 
def choose(n, m):
    return fact(n)/(fact(m)*fact(n-m))
 
def foo(n,m):
    ans = 0
 
    for num in product(range(m+1), repeat=n):
        if sum(num) == m:
            prod = fact(m)
            for x in num:
                if x>0:
                    prod *= x**(x-1) / fact(x)
            ans += prod * fact(n-1) * choose(n+m,n)
 
    return ans
 
for n in range(1,7):
    print '%d:'%n,
    print '\t'.join(str(foo(n,m)) for m in range(1,9))
 
'''
1: 2    6	24	240	3600	50400	927360	18869760
2: 6	36	240	2520	40320	705600	14515200	333849600
3: 24	240	2400	30240	524160	10644480	246758400	6346771200
4: 120	1800	25200	393120	7620480	174182400	4510598400	128731680000
5: 720	15120	282240	5443200	120476160	3073593600	88136294400	2771024256000
6: 5040	141120	3386880	79833600	2035756800	57959193600	1830744115200	63029904537600
'''
 
print '(SO)n=1:',
print '\t'.join(str(i**(i-1)*(i+1))
                for i in range(1, 9))
 
print '(SO)n=2:',
print '\t'.join(str(i**(i-2)*(2*i-1)*(i+1)*(i+2))
                for i in range(1,9))
 
print '(SO)n=3:',
print '\t'.join(str(i**(i-3)*(4*i*i-5*i+2)*(i+1)*(i+2)*(i*3))
                for i in range(1,9))
 
print '(SO)n=4:',
print '\t'.join(str(i**(i-4)*(4*i-3)*(2*i*i-3*i+2)*(i+1)*(i+2)*(i*3)*(i+4))
                for i in range(1,9))
 
'''
(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: 18.0	288.0	4140	66240	1212750	25256448	591740856	15429795840
(SO)n=4: 90.0	2160.0	41580.0	823680	17832150	426746880	11266932600	326361415680
'''
 

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