The pilot reported that on landing he touched down on the main landing gear but with the nose low. The airplane ballooned slightly, and the pilot applied power to ease the descent. The main landing gear touched down a second time and the pilot held "as much back pressure" as he could on the yoke. When the nose gear touched the ground the pilot heard a "grinding" noise and the airplane "began to buck," then veered to the left but stayed on the runway. The propeller then struck the runway, resulting in substantial damage to the firewall. When the pilot climbed out of the airplane, he observed that the nose gear tire was flat and the oleo strut was empty of fluid. The pilot reported that there was no mechanical malfunction or failure with the airplane before the accident.