Manuals/calci/PASCALTRIANGLE

PASCALTRIANGLE(r)

• $r$ is the row number.

Description

• This function gives the Coefficients of the Pascal triangle.
• In $PASCALTRIANGLE(r)$ , r is the row 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.

• This function will return the result as error when the $r\leq 0$.

Examples

• 1.PASCALTRIANGLE(1)=1
• 2.PASCALTRIANGLE(2)=1

                 1       1

• 3.PASCALTRIANGLE(3)=1

                 1       1
                 1       2         1

• 4.PASCALTRIANGLE(0)=NULL

References

• Pascal's Triangle