Originally Posted by

**robocop_911** Can anyone prove the below given identity?

I am giving it a try I also want someone else to verify!

Suppose that k and n are integers with 1<k<=n. Prove the hexagon identity

which relates terms in Pascal's triangle that form a hexagon.

$\displaystyle

\left(\begin{array}{cc}n-1\\k-1\end{array}\right) \left(\begin{array}{cc}n\\k+1\end{array}\right)

\left(\begin{array}{cc}n+1\\k\end{array}\right) =

\left(\begin{array}{cc}n-1\\k\end{array}\right)

\left(\begin{array}{cc}n\\k-1\end{array}\right)

\left(\begin{array}{cc}n+1\\k+1\end{array}\right)

$