Visualize Pascal's triangle with the product of the terms in the $n$th row

Question

How to make the following graphics by using Mathematica?

What I tried:

I used J.M's answer for the Pascal triangle

pascal = With[{n = 6}, 
Graphics[Table[
Text[Style[Binomial[n - j, n - i], Large], {2 (i - j/2), 3 j/2}], {i, n}, {j, i}]]]


product = MatrixForm[{1, 1, 2, 9, 96, 2500}

then

Show[pascal, product]

GraphicsGrid[pascal, product]

but it doesn't work.

(sequence 1, 1, 2, 9.. is the product of the terms in the $nth$ row)

Answer 1

Manipulate[

 pascal = Row[Pane[#, 50, Alignment -> Center] & /@ #] & /@ 
   Table[CoefficientList[(x + 1)^i, x], {i, 0, n - 1}];

 product = Pane @ StringPadLeft[ToString[#], 40, "."] & /@ 
   Table[(j!)^(j - 1)/BarnesG[j + 1]^2, {j, 0, n - 1}];

 Grid[{{
    Column[pascal, Center],
    Column[product, Right]
    }}, BaseStyle -> 15]
 ,
 {{n, 6}, 1, 15, 1}]