Have you encountered this famous matrix before?

[cosmicsol]

Working in a counting complexity result, it came out this n x n matrix defined as follows:

A_ij = comb(n+i-j,i) for each row i =1,...,n and each column j=1,...,n.

NOTE: comb (a,b) represents a!/(b!(a-b)!) , which is the number of subsets of size b that can selected from a set of size a.


I was wondering if anyone have seen this matrix before. I need to study the properties.

Thanks.

 

[TheIsingGuy]

nope, but just wondering what special properties does it have?

 

[cosmicsol]

This matrix appeared when i tried to prove that a counting problem was #p-complete using a polynomial interpolation technique. This matrix has full rank, and it's n-1 x n-1 upper right submatrix is equal to A(n-1).