# how to calculate nth term of mth row of this table?

there is a table which grows as

1,1
1,1,2
1,1,3,3
1,1,4,4,6
1,1,5,5,10,10
1,1,6,6,15,15,20
.....and so on


If i want to find an specific element of the table like if i want to find 4th element of 6th row then the answer will be 6 but if i want to find the nth element of mth row for any n>=1,m>=1 then how to do it?

• Hi! Do you know this? – MattAllegro Feb 22 '15 at 17:37

## 1 Answer

The $n$-th row contains the binomial coefficients $\binom{n}{0}$, ..., $\binom{n}{n}$, sorted by size. The $k$th element of the $n$th row is therefore given by $$\binom{n}{\lfloor \frac{k-1}{2} \rfloor}.$$

• Small correction: With $k$ from $0$ to $n$, this will work if you use the floor function as $\displaystyle\binom{n}{\big\lfloor \frac{k}{2} \big\rfloor}$. Alternatively, it works with the ceiling function as $\displaystyle\binom{n}{\big\lceil \frac{k-1}{2} \big\rceil}$. – J. W. Perry Feb 22 '15 at 18:30
• And I do mean to say, you have miswritten your formula. – J. W. Perry Feb 23 '15 at 0:46