The coin-flip puzzle

You flip a coin x times. You keep track of a counter, n. Each time you flip heads, you add one, and each time you flip tails you subtract one. The expected absolute value of n is some function f(x). That function aproaches some constant (a constant is a number like 4, or pi) multiplied by a very common function in math. What is that constant? When you find the solution, email it to Leo. No cheating by looking anything up on the internet!