I am solving a problem in which at some point i need to find answer for this sequence, when $$$n$$$ is known.

$$$n\times(n + 1) \; + \; (n - 1)\times n \; + \; (n - 2)\times (n - 1) \; + \; (n - 3)\times (n-2) \ldots 1\times 2$$$

it has $$$n$$$ terms.

Ans = $$$\frac{n \times (n + 1) \times (n + 2)}{3}$$$

thanks sam_2912 for help.