here is link to Pascal's rule at wikipedia
Pascal's rule - Wikipedia, the free encyclopedia
its written as
if we plug in k=n+1 , we get
is something wrong ?
Some authors define
whenever it is not true that .
See, for example, Knuth, "The Art of Computer Programming, Vol 1", or
Binomial Coefficient -- from Wolfram MathWorld.
By this definition, it is correct to say that