check Subsets Summing | Python Fiddle

#    F(1) = 1                                           =1
#               3        3                              =6                    /5
#    F(2) = ((1)+(2))+((1+2))
#                 6                12             6     =24                   /18
#                 6          3     4     5        6             
#    F(3) = ((1)+(2)+(3))+((1+2)+(1+3)+(2+3))+((1+2+3))
#                 10                           30                                   30                               10    =80       / 56
#    F(4) = ((1)+(2)+(3)+(4))+((1+2)+(1+3)+(2+3) + (1+4)+(2+4)+(3+4) )+ ((1+2+3) + (1+2+4)+ (1+3+4) + (2+3+4)) +((1+2+3+4))
#    
#                     /5                                                         20+10= /30                                      
#                  
#    F(5) = ((1)+(2)+(3)+(4)+(5)) + ((1+2)+(1+3)+(2+3)+(1+4)+(2+4)+(3+4) + (5+1)+(5+2)+(5+3)+(5+4)) 
#          30+(1*3+2*3+3*3+4*3)=30+17+12=30+29= /59 
#
# + ((1+2+3)+(1+2+4)+(1+3+4)+(2+3+4) + (1+2+5) + (1+3+5) + (1+4+5) + (2+3+5) + (2+4+5) + (3+4+5))

from math import factorial

levels = {0:0}

def G(n):
    summary = 0
    for i in range(1,n+1):
        summary+=F(i)
    return summary

def F(s):
    
    levels[s] = combination_additional_sum(s) + levels[s-1]
    
    return levels[s]

def combination_additional_sum(f_num):
    summary = 0
    for l in range(1, f_num+1):
        print 'l:',l
        print 'summary:', summary
        if(l==1):
            print 'l==1, summary+=', f_num
            summary += f_num
        elif(l==f_num):
            sum_temp = sum(i for i in range(1,f_num+1))
            print 'l==f_num, summary+=', sum_temp
            summary += sum_temp
        else:
            summary += comb_part_sum(f_num, l)
        
        
    return summary
        
def comb_part_sum(f_num, comb_count):
    print 'comb_level_sum'
    print '   f_num',f_num
    print '   ccomb_count', comb_count
    
    summary = 0
    
    	
    #multiplier = comb_count-1
    multiplier = factorial(f_num-1)/(factorial(comb_count-1)*factorial(f_num-comb_count))/(f_num-1)
    print '   multiplier', multiplier
    
    #summary += f_num
    #summary += sum(i for i in range(f_num))
    
    for i in range(1, f_num):
        print '   i:',i
        print '   i*multiplier:',i*multiplier
        summary += i*multiplier

summary +=f_num*(f_num-1)

print '   comb_level_sum return=', summary    
    return summary

f_num =4
print f_num,':',combination_additional_sum(f_num)
#print f_num,':',G(f_num)
print levels

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