Matrix Log of Triangle A051731=A054525^-1

[franktaw at netscape.net]

I think this is exactly the way to do it.
 
The only real alternative is to submit two sequences, with the numerators and denominators.  I would only do that in this case if there is some independent interest in the table of zeros and ones which constitutes the numerators.  Is there? 
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
 
 
-----Original Message-----
From: Paul D. Hanna <pauldhanna at juno.com>
To: seqfan at ext.jussieu.fr
Sent: Tue, 10 Jan 2006 01:53:45 -0500
Subject: Matrix Log of Triangle A051731=A054525^-1


Seqfans, 
       How would one submit the following triangle of UNIT FRACTIONS 
that is aerated with many ZEROS? 
 
...
  
The matrix log of triangle A051731 begins:
0;
1,0;
1,0,0;
1/2,1,0,0;
1,0,0,0,0;
0,1,1,0,0,0;
1,0,0,0,0,0,0;
1/3,1/2,0,1,0,0,0,0;
1/2,0,1,0,0,0,0,0,0;
0,1,0,0,1,0,0,0,0,0;
1,0,0,0,0,0,0,0,0,0,0; ...
 
Which consists entirely of unit fractions and zeros.
 
If we list only the denominators of the unit fractions of the non-zero
entries, 
and leave zero entries alone, we get the triangle defined by:  
*  T(n,k) = A100995(n/k) when k|n, 0 otherwise. 
    
But what about at all those zeros ... 
Being a matrix log, I would hate to leave out any zeros ...
  
Row#: Row elements;
1: 0;
2: 1,0;
3: 1,0,0;
4: 2,1,0,0;
5: 1,0,0,0,0;
6: 0,1,1,0,0,0;
7: 1,0,0,0,0,0,0;
8: 3,2,0,1,0,0,0,0;
9: 2,0,1,0,0,0,0,0,0;
10: 0,1,0,0,1,0,0,0,0,0;
11: 1,0,0,0,0,0,0,0,0,0,0;
... 
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