Manuals/calci/PASCALTRIANGLE

PASCALTRIANGLE (Levels)

is the level number of the Pascal Triangle.
- PASCALTRIANGLE(), is a triangle of numbers in which a row represents the coefficients of the binomial series.

Description

This function gives the Coefficients of the Pascal triangle.
In $PASCALTRIANGLE(Levels)$ , $Levels$ is the level number of the Pascal triangle.
Pascal triangle is the arrangement of numbers of the Binomial coefficients in a triangular shape.
It is started with the number $1$ at the top in the 1st row.
Then from the 2nd row each number in the triangle is the sum of the two directly above it.
The construction is related to the Binomial Coefficients by Pascal's rule is :

$(x+y)^{n}=\sum _{k=0}^{n}{\binom {n}{k}}x^{n-k}.y^{k}$ . where ${\dbinom {n}{k}}$ is the binomial coefficient.

                 1   
                 1       1

                 1    
                 1       1
                 1       2         1