I am surprised at the responses from Bimpel and Tony. I think Bimpel is incorrect, while Jansen got it right. As for Tony's response, he starts out saying R1 is redundant and possibly an error, and then the rest of that same sentence says exactly why R1 is needed.
I agree that one of the reasons given for the added resistor, that it pulls the capacitor voltage up to Vcc or closer to Vcc, is wrong. However, the resistor does compensate for a characteristic of the bipolar 555 output stage, and improves the circuit performance.
The standard 555 equations assume that the output swings between 0.000% of Vcc (GND) and 100.000% of Vcc. In real life, both assumptions are wrong. While the CMOS version is better than the bipolar version, both types have an output that is not perfect; the high output (Vhi) is some number of volts less than Vcc, and the low output (Vlo) is some different number of tenths of a volt above GND. Again, the CMOS part is much better, so this discussion primarily is about the bipolar part.
While it is true that the timing capacitor voltage oscillates between 1/3 and 2/3 Vcc, and never approaches either rail, that is not the point. The point is that the charging/discharging currents are dependent on the voltages across the timing resistor. These are the voltage difference between 2/3 Vcc and Vlo, and the difference between 1/3 Vcc and Vhi. Because the 555 high and low output voltages are not symmetrical in their distances from their respective rails, the charging and discharging currents are not equal. Thus, the circuit does not produce a 50/50 square wave.
The CMOS 555 is much better at this, as its output headrooms or margins are very close to equal. But the bipolar 555 is worse. As above, Vhi can be over 2 volts below Vcc, while Vlo is around 0.5 V above GND. This is the reason for the added resistor from the timing capacitor directly to Vcc - it pees in a small current so that the total charging current is closer to the discharge current. This makes the output duty cycle closer to 50/50.
There is no way to calculate an exact value for the added resistor, because the output stage headroom requirements change with output load current, with temperature, and from part to part due to process variations. An approximate value or starting point can be determined using the parameters in the datasheet.