# Thread: Relation between the terms of series

1. ## 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.

2. 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

3. These are the terms for $\binom{2n}{n}$ for $n=1,2,3,........$.

4. Originally Posted by Sambit
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.

5. 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 $a[n+1] = \frac{4n+2}{n+1}a[n].$

6. 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

7. Originally Posted by Opalg
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