MATLAB: General Binomial Matrix Manipulation

MATLABmatrixmatrix manipulation

Let's say I have a matrix of the form:

Starting from this matrix, I would like to calculate a new matrix, in a time efficient way:

The algorithm, which I am looking for, should also work for a matrix of the form:

Does someone know how this algorithm could look like?

Best

Alex

[m,n]=size(Astart);
B=reshape(Astart,m,1,n).*Astart;
Aend=reshape(B,m,[]);

M(:,2:end) = M(:,2:end)+1

V = ones(1,size(M,2));
V(1) = 0;
M = bsxfun(@plus,M,V)

Let's give the matrix we're operating on [1 2] a name. Let's say

A = [1 2];

Then repmat repeats A in a two-by-two arrangement:

repmat(A,2,2)
ans =
   1     2     1     2
   1     2     1     2

Then reshape it into a 1-by-however-wide-it-needs-to-be matrix:

reshape(ans,1,[])
ans =
   1     1     2     2     1     1     2     2