Wikipedia:Math

My formula:

 

...where   is the r'th integral


The traditional formula:

 

...where   is a Permutation


For example:

 

Which is the same as:

 


If you consider:

 

and:

 

and:

 

...then it all logically falls out.

New notation

edit

Lets use   meaning the expression   occurs n times using different variables for a, all summed together.

So  .

For instance:

 

Could be written as:

 

 

These numbers can be gleaned from the following Pascal's tetrahedron layer:

   1
  3 3
 3 6 3
1 3 3 1

And so...

 

     1
    4  4
   6 10  6
  4 10 10 4
 1 4  6  4 1