What are the names of the rows in pascal's triangle.?

Question

They have specific names for some reason. I can only get up to this fifth row. Then it stumbles me. Like for example natural numbers are 12345.

What are the names of the diagonal rows in pascals triangle is what im really after?

Triangular Numbers are for example 1 3 6 10 15
Tetrahedral numbers are for example 1 4 10 20 35
Pentatope Numbers are for example 1 5 15 35 70

Answer 1

They are usually just numbered, starting at row 0.

Row 0 = 1
Row 1 = 1 1
Row 2 = 1 2 1
Row 3 = 1 3 3 1
Row 4 = 1 4 6 4 1
Row 5 = 1 5 10 10 5 1
etc.

Similarly, the items in each row are numbered 0, 1, 2, 3, ..., n

For example, if someone asked you for row 4, item 2, it would be the number 6.

A formula for C(n, k) is:
.... n!
------------
k! (n-k)!

Using the example above C(4, 2) =
.... 4!
-----------
2! (4-2)!

. 24
-------
2 * 2

= 24/4

= 6

Quote:
"I don't care what you call me, as long as you don't call me late to dinner" :-)

Edit:
For the diagonals (not rows) they form the triangular numbers, tetrahedral numbers, pentatope numbers, etc. These are either called polygonal numbers, or figurate numbers.

Answer 2

The Pascal triangle gives the coefficient of the expansion of a binary, say (a + b). The initial one is for exponent 0, the next row is for exponent 1, then 2 , then 3 , etc

I can not recall if there is a name given to the rows..

Answer 3

the row has a name?