RC circuit with a transistor and an LED

Could someone please explain how this circuit works?
I understand that while the capacitor is charging, current flows
to the base of transistor and so the LED lights, but I can't figure
out the discharging.

P.S. I assume that by building this circuit I'll get an LED blinking constantly?

The LED starts ON, then goes off and stays off. When the supply is applied to the capacitor, the voltage across its pins cannot change instantaneously, the voltage on one side = supply volts, so the voltage on the OTHER side = supply volts, so the base of the transistor goes high, and the LED lights. NOW current flows into the capacitor via the resistor, and the voltage on the lower plate FALLS, eventually turning the LED off.

No blinking happens.