AC transformer for LED
Since the output frequency of a full-wave rectifier will be twice its input frequency, making flicker a non-issue, the easy way is to use a full-wave bridge with no smoothing (since its output frequency will be either 100 or 120 Hz ) and to connect the LEDs in series with an appropriate ballast.

For example, in the schematic, following, 120 volt 60 Hz mains are stepped down to about 12 volts RMS and used to drive a single LED through a 420 ohm resistor. 

The transformer puts out about 17 volts, peak, and there are two diode drops across the bridge, so that leaves about 16 volts peak, which is about 11 volts RMS, across D5 and R1.

D5 drops about 2.5 volts RMS with 20 mA through it, which leaves 8.5 volts RMS across the resistor.

So, to get the value of the resistor, we can say:
$$ R = \frac{E}{I} = \frac{8.5V}{0.02A}=425\Omega $$

For more LEDs, you'd change the transformer's secondary voltage and possibly the bridge diodes and adjust the ballast to suck up whatever excess voltage was there that the LEDs didn't need.

Just for grins, Here's the LTspice .asc file you can run to play with the circuit if you want to.