Kayla Straub And A Pile Of Stones

Kayla Straub starts with a pile of 15 stones. She divides the pile into two new piles and nds the product of the numbers of stones in the two new piles. Kayla then divides one of the existing piles into two new piles. She ends the product of the numbers of stones in the two new piles and adds it to the previous product. Kayla continues this process, each time adding the product of the numbers of stones in the two new piles to the previous total, until she has 15 piles with one stone each. What is the greatest possible ending total?

This problem is a part of the series Greatest MathsCount Problems Ever