I wonder now how it looks in general case, i.e. if you have (x^n + x^(n+1)+...+x)^n.
I wonder if you can express those Pascal's triangles in similar way as the simple Pascal's triangle, i.e. {n \choose k} and etc. Then it would be possible to express it as a Riemann sum!
Anyways, this is very beautiful, I also like these magic of numbers in mathematics.
This work is derived from the other one I am working on. But I think it's the beginning for these triangles, please share it as it's the way you can discover special properties like Pascal's and more because of its growing configuration.