Exact computations with large integers are possible, simple, efficient, and reliable with Mathematica. Download the notebook, try the calculation, and check it for yourself doing it by hand.

You can change 20 to 100 or 500 if you want….

The sequence is defined by its first term and a computational process that allows the computation of , , etc.:

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Once you have computed for some , then all values from 0 to are remembered by Mathematica.