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Pascals Triangle Manipulation

  1. Feb 13, 2008 #1
    Here is the manipulation of Pascals Triangle. I'm trying to figure out a way to represent these rows in terms of a combination. Check it out...



    1
    1 1
    1 4 1
    1 9 9 1
    1 16 36 16 1
    1 25 100 100 25 1
    .
    .
    .
     
  2. jcsd
  3. Feb 13, 2008 #2

    mathman

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    Science Advisor
    Gold Member

    Why have you posed this?

    (nCk)2
     
  4. Feb 13, 2008 #3
    Is there any particular pattern also with the sum of the rows as well?

    The reason is because it's part of a problem I'm working on regarding two people at opposite corners on a massive n by n board. On player can only move north and east, the other south and west. Basically, I need to find the expected value of the number of times they will meet, and I have a hunch this plays a part in. Thanks!
     
  5. Feb 13, 2008 #4
    See A000984.
     
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