I'm trying to create and populate the Array `A` with a sequence of lower triangular matrices based on the following relation:
A[k+1][i,j] = a (1+k) A[k][i,j] + b ((1+j) A[k][i-1,j] - j A[k][i-1,j-1])
The rows and columns of each matrix are given by i and j; a and b are scalars. The structure of A is not important provided a matrix can be accessed for a given k. The highest k value will not be more than about 100.
The starting matrix for k=1 is
[ 1 -1]
Any guidance on where to start with setting up the appropriate procedure would be greatly appreciated.