Borrowing `triangularArrayLayout` from [here][1], I have:

    triangularArrayLayout[triArray_List, opts___] := 
     Module[{n = Length[triArray]}, 
      Graphics[MapIndexed[
        Text[Style[#1, 
           Large], {Sqrt[3] (n - 1 + #2.{-1, 2}), 3 (n - First[#2] + 1)}/
           2] &, triArray, {2}], opts]]
    
    n = 6;
    s = 500;
    coeffs = triangularArrayLayout[Table[Row[{"C(", i, ",", j, ")"}], {i, 0, n}, {j, 0, i}], 
       ImageSize -> s];
    tri = triangularArrayLayout[Table[Binomial[i, j], {i, 0, n}, {j, 0, i}], 
       ImageSize -> s];
    layers = {Overlay[{coeffs, Show[tri, TextStyle -> GrayLevel[.8]]}, Alignment -> Top], 
       Overlay[{tri, Show[coeffs, TextStyle -> GrayLevel[.8]]}, Alignment -> Top]};

    Manipulate[layers[[u]], {{u, 1, " "}, {1 -> "binomial coefficients", 
       2 -> "Pascal's triangle"}}, ControlType -> RadioButtonBar]

but the vertical alignment is off:

![Mathematica graphics](https://i.sstatic.net/fZooA.png)
![Mathematica graphics](https://i.sstatic.net/L0LM5.png)

This is the main issue, but I am also curious how to:

1. typeset the $C(n,r)$ as `TraditionalForm` (with the varying $n$ and $r$ values throughout)
2. typeset the $C(n,r)$ as $_{n}C_{r}$ (also with the varying $n$ and $r$ values).


  [1]: http://mathematica.stackexchange.com/questions/9959/visualize-pascals-triangle-and-other-triangle-shaped-lists