# Relation between the terms of series

• Mar 13th 2011, 07:20 AM
pranay
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.
• Mar 13th 2011, 07:45 AM
CaptainBlack
Quote:

Originally Posted by pranay
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
• Mar 13th 2011, 07:56 AM
Sambit
These are the terms for $\displaystyle \binom{2n}{n}$ for $\displaystyle n=1,2,3,........$.
• Mar 13th 2011, 11:09 AM
pranay
Quote:

Originally Posted by Sambit
These are the terms for $\displaystyle \binom{2n}{n}$ for $\displaystyle n=1,2,3,........$.

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.
• Mar 13th 2011, 11:59 AM
Opalg
Quote:

Originally Posted by pranay
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 $\displaystyle a[n+1] = \frac{4n+2}{n+1}a[n].$
• Mar 13th 2011, 02:52 PM
CaptainBlack
Quote:

Originally Posted by pranay
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
• Mar 13th 2011, 07:26 PM
pranay
Quote:

Originally Posted by Opalg
These numbers are closely related to the Catalan numbers. They satisfy the recurrence relation $\displaystyle a[n+1] = \frac{4n+2}{n+1}a[n].$

Thanks a lot :)