What is the equation for predicting the middle number in Pascal's triangle?

[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?

 

[robphy]

Can you give explicit examples of "middle number" ?
http://www.wolframalpha.com/input/?i=pascal+triangle [click on the "More rows" button]

 

[SteamKing]

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.

 

[gnome222]

Can you give explicit examples of "middle number" ?
http://www.wolframalpha.com/input/?i=pascal+triangle [click on the "More rows" button]

numbers 2, 6, 20, 70, 252

 

[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]

numbers 2, 6, 20, 70, 252

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

 

[robphy]

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

numbers 2, 6, 20, 70, 252

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

https://www.wolframalpha.com/input/?i=(2n)!/(n!*n!) (Values... click on "More values")
Cool.. https://oeis.org/A000984