Nikica if you want a precise timer, a 555 relies on stable supply voltage, a trimpot and very expensive large capacitors with very low leakage., making this design impractical due to the fact that most big caps have a self leakage in this range of time and going to an ultracap with long leakage time constants gets more expensive.
The traditional solution for this is to use a CD4020 counter that runs at a higher frequency and has ripple binary counters /2, /4 /8.... than can be gated to any combination to give a binary decoded output using logic gates to synthesize the result.. ANother method is use a 4017 decade Johnson counter with a /2 counter in front to gate clock and 1 bit out to get 1/20 duty cycle and then vary the clock using a much easier 1 Hz clock to generate the pulse. THen of course there is a PIC, 1 chip MCU approach and many others.
added ...
a low cost Alum polymer cap at 1000uF 6V has leakage of 630uA thus with a 1V charge decay time constant is I=C dV/dt or dt= C dV/I = 1e-3 *1/0.63e-3 or around 1.6 second , so that wont work.
https://www.digikey.ca/product-detail/en/RR70J102MDN1/493-3710-ND/2207246
a high cost ultracap or supercap...
$3
https://www.digikey.ca/product-detail/en/PAS3225P3R3113/587-3260-1-ND/3662201 has no leakage specs
The longest time constant due to leakage in caps are FILM but due to density are small in value or huge in price.
If you find a cap that has < 10uA of leakage in this range of uF, you could use a Schmitt trigger Astable oscillator using R+Diode in parallel with 20R to get the asymmetrical pulse.
Or better use a precision comparator with precision R ratios above to create quick ramp down and slow ramp up to create 1sec High and 20 second low repeating. A current source is more stable.