Is row 14, column 4 for pascals triangle is 186?

434 Views Asked by At

In an answer in question in here diagram depicting pascals triangle ,I do not understand why in 14th row entries given are: $1, 13, 78, 186$ etc, is $186$ a typo?

Because:

$$1 \times \frac{13+1-1}1 = 13.0$$ $$13 \times \frac{13+1-2}2 = 78.0$$ $$ 78 \times \frac{13+1-3}3 = 286.0$$

If $186$ is not a typo, can some please explain why is this the case? Above calculations are from "Calculating a row or diagonal by itself" section of wiki page for pascals triangle.

It is appropriate put it as comment in the question, I joined stack exchange few minutes and I don't have the privilege to do so.

3

There are 3 best solutions below

0
On BEST ANSWER

Yes, that's a typo. Apart from your calculation, it should also be the sum of the two numbers, above, $66+220=286$.

0
On

Row $14$ column $4$ is $\binom{13}{3} = 286$ so yes, it's a typo.

4
On

Prime $13$ does not divide $186$ so it must be a typo.