# Pattern in pascal's triangle

## Main Question or Discussion Point

I am trying to find the equation to predict the next middle number in pascal's triangle. By middle number I mean in each row that has odd number of numbers the middle number of that row. So for example row 6 which has 1,6,15,20( middle number), 15,6,1. I am trying to find that middle number, but without any luck. Any suggestions?

robphy
Homework Helper
Gold Member
SteamKing
Staff Emeritus
Homework Helper
I am trying to find the equation to predict the next middle number in pascal's triangle. By middle number I mean in each row that has odd number of numbers the middle number of that row. So for example row 6 which has 1,6,15,20( middle number), 15,6,1. I am trying to find that middle number, but without any luck. Any suggestions?
Look at the row immediately preceding, that is row 5. Do you notice anything special relating the numbers in row 5 to the numbers in row 6? The first and last number in each row is, of course, 1.

Last edited:
Svein
You know that the number in Pascal's triangle, row n, place k (k=0 to n), is given by $\frac{n!}{k!(n-k)!}$?

Svein