W. Lang Sep 24 2008

A144879 tabf array: partition numbers  M31(-5).

Partitions of n listed in Abramowitz-Stegun 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       5       1      0      0       0      0       0       0       0       0      0      0      0      0     0     0     0     0    0    0    0   0 
 
   3      20      15      1      0       0      0       0       0       0       0      0      0      0      0     0     0     0     0    0    0    0   0
    
   4      60      80     75     30       1      0       0       0       0       0      0      0      0      0     0     0     0     0    0    0    0   0  
 
   5     120     300   1000    200     375     50       1       0       0       0      0      0      0      0     0     0     0     0    0    0    0   0 
        
   6     120     720   4500   4000     900   6000    1875     400    1125      75      1      0      0      0     0     0     0     0    0    0    0   0  
 
   7       0     840  12600  42000    2520  31500   28000   52500    2100   21000  13125    700   2625    105     1     0     0     0    0    0    0   0  
   
   8       0       0  16800 134400  126000   3360  100800  336000  315000  560000   6720 126000 112000 420000 65625  4200 56000 52500 1120 5250  140   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 ...     
    


The next two rows, for n=9 and n=10, are:

n=9: [0, 0, 0, 201600, 907200, 0, 151200, 1209600, 1134000, 1134000, 7560000, 2240000, 10080, 453600, 1512000, 2835000, 5040000, 3150000, 15120, 378000, 336000, 1890000, 590625, 7560, 126000, 157500, 1680, 9450, 180, 1],

n=10:  [0, 0, 0, 0, 1512000, 1814400, 0, 0, 2016000, 9072000, 1890000, 30240000, 28350000, 50400000, 0, 
756000, 6048000, 5670000, 11340000, 75600000, 22400000, 23625000, 63000000, 25200, 1512000, 5040000, 
14175000, 25200000, 31500000, 2953125, 30240, 945000, 840000, 6300000, 2953125, 12600, 252000, 393750, 
2400, 15750, 225, 1].

The row sums give, for n>=1: A049431 = [1,6,36,246,2046,19716,209616,2441916,31050396,425883816,...].
They coincide with the row sums of triangle A049411 = S1(-5).


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