Matrix – Meaning of ## #

While looking for an answer to a different problem, I found the following example:

In[1]: = Array[Plus[##] &, {2,2}]Outside[1]= {{2,3}, {3,4}}

Having read the documentation of the Space Y SlotSequence, I understand the previous example. If we consider it as a matrix. $ M_ {ij} $, take the two indexes and add them, $ M_ {ij} = i + j $. I also understand that it is equivalent to Training[Plus[#1,#2] &, {2, 2}].

I tried to make the expression a bit more complicated:

In[2]: = Array[Plus[##,#] &, {2,2}]Outside[2]= {{3,4}, {5,6}}

that acts as $ M_ {ij} = (i + j) + i $, or if we replace the last # with # two, $ M_ {ij} = (i + j) + j $.

Now, I'm really stuck in the interpretation:

In[3]: = Array[Plus[## #] &, {2,2}]Outside[3]= {{1,2}, {4,8}}

What is the corresponding expression for $ M_ {ij} $?