W. Lang, Sep 19 2008

A107106 tabf array: partition numbers M31hat(1) (W.L. notation) is  M_2/M_3 (A-St notation). Row n is filled with zeros for k>p(n), the partition number.

Partitions of n listed in Abramowitz-Stegun (A-St) order p. 831-2 (see the main page for an A-number with the reference).

 
   n\k        1         2        3        4        5        6        7        8       9      10       11      12      13      14     15     16     17     18    19   20  21 22 ... 
                                                                                                              
          
   1          1         0        0        0        0        0        0        0       0       0        0       0       0       0      0      0      0      0     0    0   0  0 
     
   2          1         1        0        0        0        0        0        0       0       0        0       0       0       0      0      0      0      0     0    0   0  0 
        
   3          2         1        1        0        0        0        0        0       0       0        0       0       0       0      0      0      0      0     0    0   0  0
    
   4          6         2        1        1        1        0        0        0       0       0        0       0       0       0      0      0      0      0     0    0   0  0  
 
   5         24         6        2        2        1        1        1        0       0       0        0       0       0       0      0      0      0      0     0    0   0  0 
        
   6        120        24        6        4        6        2        1        2       1       1        1       0       0       0      0      0      0      0     0   0    0  0 

   7        720       120       24       12       24        6        4        2       6       2        1       2       1       1      1      0      0      0     0   0    0  0

   8       5040       720      120       48       36      120       24       12       6       4       24       6       4       2      1      6      2      1     2   1    1  1
   .    
   . 
   .
 
   n\k        1         2        3        4        5        6        7        8       9      10       11      12      13      14     15     16     17     18    19   20  21 22 ..  
 


n=9: [40320, 5040, 720, 240, 144, 720, 120, 48, 36, 24, 12, 8, 120, 24, 12, 6, 4, 2, 24, 6, 4, 2, 1, 6, 2,
 1, 2, 1, 1, 1],

n=10: [362880, 40320, 5040, 1440, 720, 576, 5040, 720, 240, 144, 120, 48, 36, 24, 720, 120, 48,
 36, 24, 12, 8, 6, 4, 120, 24, 12, 6, 4, 2, 1, 24, 6, 4, 2, 1, 6, 2, 1, 2, 1, 1, 1]. 


The first column gives (n-1)!= A000142(n-1), n>=1, (factorials).

The row sums give for n>=1: A107107.
They coincide with the row sums of triangle A144351.



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