Electronic – Slow build-up and discharge LED effect

I was trying to build a circuit that if switched on would slowly (in span of of 1~5s) light up around 20 LEDs – progressively, not all at once.

To achieve that i used one capacitor to initiate the "build up" effect (and discharge when switched off) and then used NPN transistor's emitter as a base input for next transistor, as shown on diagram below.

It works but with each consecutive "part" the light is dimmer and fades out completely after 3rd LED. Which leads me to suspect that power on base of transistor is getting weaker – but it shouldn't require much to let power through.

Transistors i have used are BC337-25.

Resistors vary, i was experimenting with different ones but R1 is 1.5k Ohm, R2 is 100k Ohm, resistors between emitters and LEDs are 220 Ohm, and one between emitters and bases are 1k Ohm

As for Voltages, both inputs are currently 3.3V, but final version will be charged off one 3.9V 18650 battery.

The question is: is it possible to achieve that gradually lighting up effect (similar to "percentage charged") with this design, and if yes what is the problem with my design?

Note that while I only have some understanding of a topic I did my research around the Internet was unable to find good enough resources that I could apply to my problem.