Matrices and INVERTi of m-tuple Factorials

[Paul D. Hanna]

Dear Seqfans,
        I would like to share with you a family of interesting triangular
matrices 
and associated sequences. 
 
Some of the properties of these matrices are: 
o column sequences involve the INVERTi of m-tuple factorials, such as
double and triple factorials; 
o the matrix inverse is simple, with secondary diagonal={m,2m,3m,4m,...};

o the matrix powers of the triangles have interesting patterns; 
o an integer matrix logarithm exists (which I find quite unexpected). 
 
The following examples involve m-tuple factorials for m=1,2,3,
respectively.
 
Case m=1:
http://www.research.att.com/projects/OEIS?Anum=A104980
Case m=2:
http://www.research.att.com/projects/OEIS?Anum=A105615
Case m=3:
http://www.research.att.com/projects/OEIS?Anum=A107717
 
The pattern can be generalized to other triangles and sequences for m>3;
and if anyone finds these interesting, they are welcome to submit cases 
for m=4 (INVERTi of quadruple factorials) or higher 
(note: the pattern continues for negative m as well).
 
I believe that several of the sequences generated by the matrix
formulation 
are significant and will be found to have combinatorial interpretations. 
   
Regards,
     Paul