A Dollar Your Way

I've long been an amateur U.S. coin collector, and have always been interested in the changes that they've gone through over the years. One thing that has not changed over the last century is the number of different ways to make change for a dollar. And that's what leads to today's Free-for-all Friday  challenge at the mentalfloss.com Brain Game. Good luck:

How many different ways are there to make change for a one-dollar bill using some combination of half-dollars, quarters, dimes, nickels, and pennies? Not every coin type need be used in every combination, but each combo should total exactly $1 in coins. Here is the ANSWER.

How many different ways are there to make change for a one-dollar bill using some combination of half-dollars, quarters, dimes, nickels, and pennies?

ANSWER:  292.

Here's a years-old (but still great) Web page that provides details. Note that my question did NOT include the possibility of a one-dollar coin as being valid change for a one-dollar bill. Have a great weekend!