The Doubling Coin Game With No Fair Price

A dealer offers the following classic gamble. She flips a fair coin over and over, stopping at the first heads. If that first heads lands on flip number $n$, she pays you $\$2^n$ — so \$2 if heads comes immediately, \$4 if it takes two flips, \$8 for three, and so on. What entry fee would make this game actuarially fair?