# Pattern in pascal's triangle

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1. Apr 19, 2015

### gnome222

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?

2. Apr 19, 2015

### robphy

3. Apr 19, 2015

### SteamKing

Staff Emeritus
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.

4. Apr 19, 2015

### gnome222

Last edited: Apr 19, 2015
5. Apr 20, 2015

### Svein

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

6. Apr 20, 2015

### Svein

And then: 924, 3432, 1287, 48620, 184756, 705432

7. Apr 20, 2015

### robphy

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