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Pattern in pascal's triangle

  1. Apr 19, 2015 #1
    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. jcsd
  3. Apr 19, 2015 #2

    robphy

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  4. Apr 19, 2015 #3

    SteamKing

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    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.
     
  5. Apr 19, 2015 #4
    Last edited: Apr 19, 2015
  6. Apr 20, 2015 #5

    Svein

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    You know that the number in Pascal's triangle, row n, place k (k=0 to n), is given by [itex]\frac{n!}{k!(n-k)!} [/itex]?
     
  7. Apr 20, 2015 #6

    Svein

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    And then: 924, 3432, 1287, 48620, 184756, 705432
     
  8. Apr 20, 2015 #7

    robphy

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