To be honest I'm not convinced there is a nice equation that describes the pattern of increase. Looking at the numbers and how it increases in an excel spreadsheet show some weird jumps where it either jumps up by a lot more then it was or even decreases how much experience is required for the next level.
It kind of feels like someone was playing with an equation but wanted the numbers to look nicer so they manually adjusted them for various reason such as wanting them to be rounded off nice after the increases, but then needed to pull the increase back into line after doing that.
Being a math person I'm curious myself, but at least initially looking at it I'm not convinced there is an equation that will do what you want. Maybe an equation with a list of rules... maybe.