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Math Help - Relation between the terms of series

  1. #1
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    Relation between the terms of series

    Hi, i can't find a relation between the terms of the following series:
    (i.e how to get the next term by relating to previous term(s).)
    The series is:
    2,6,20,70,252,924,3432,...
    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by pranay View Post
    Hi, i can't find a relation between the terms of the following series:
    (i.e how to get the next term by relating to previous term(s).)
    The series is:
    2,6,20,70,252,924,3432,...
    Thanks.
    You type it into the >>Online Encyclopaedia of Integer Sequences<<.

    Then you note that there is no unique solution to such questions. In fact the only correct answer is "What would you like it to be"

    CB
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  3. #3
    Senior Member Sambit's Avatar
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    These are the terms for \binom{2n}{n} for n=1,2,3,.........
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    Quote Originally Posted by Sambit View Post
    These are the terms for \binom{2n}{n} for n=1,2,3,.........
    That i noticed from the link provided above, actually i was looking for some relationship between the consequtive elements, i.e how a[i] is related to a[i-1] (if there exists such relationship).
    Thanks.
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  5. #5
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    Opalg's Avatar
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    Quote Originally Posted by pranay View Post
    I was looking for some relationship between the consecutive elements, i.e how a[i] is related to a[i-1] (if there exists such relationship).
    These numbers are closely related to the Catalan numbers. They satisfy the recurrence relation a[n+1] = \frac{4n+2}{n+1}a[n].
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by pranay View Post
    That i noticed from the link provided above, actually i was looking for some relationship between the consequtive elements, i.e how a[i] is related to a[i-1] (if there exists such relationship).
    Thanks.
    And if you look at the link more closely you will see that it listed at least three possibilities.

    CB
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  7. #7
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    Quote Originally Posted by Opalg View Post
    These numbers are closely related to the Catalan numbers. They satisfy the recurrence relation a[n+1] = \frac{4n+2}{n+1}a[n].
    Thanks a lot
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