If I were you Tim, rather than doubling the recipe, I would increase the amounts of every ingredient by 1/2, so make 1 and 1/2 times the recipe. This should give you just what you want. I use this formula whenever I’m increasing the size of the pan from 2- 8” pans to 2-9” pans or 1- 9”x13” pan with great success. If you double the recipe you will end up with too much batter and will either have to put some of the extra in another smaller pan, or take your chances of the cake oveflowing if you put it all into the 10”x15” pan.
So, for instance, instead of 1 1/2 cups sugar, use another 3/4 cup sugar, or a total of 2 1/4 cups. For the egg, since its difficult to divide an egg in half, go ahead and use 2 eggs. Convert you recipe this way, and write the amounts down for future reference.
HTH,
Eddie