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 ${\binom {n}{k}}$ 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

1. PASCALTRIANGLE(3)=1

                 1       1
                 1       2         1

1. PASCALTRIANGLE(0)=NULL

References

• Pascal's Triangle

PASCALTRIANGLE(level)

where

level is any real number

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PASCALTRIANGLE function returns pascal's triangle for the given level.

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PASCALTRIANGLE returns NaN if level is not a real number.

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PASCALTRIANGLE

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Lets see an example in (Column2Row1)

?UNIQ9eec20026ff870ff-nowiki-00000002-QINU?

Returns 1,1,1,1,2,1 for PASCALTRIANGLE(3)

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Syntax

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Remarks

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Examples

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Description

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Default Calci

	Column1	Column2	Column3	Column4
Row1	3	1,1,1,1,2,1
Row2		File:Copy-cube.gif
Row3
Row4
Row5
Row6

File:Calci1.gif

$

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