If you have a series of numbers (where the first number corresponds to the index **zero**):

$$ \frac{1}{2}+ \frac{1}{24}+ \frac{1}{720}+... $$

Is there a systematic way to work backwards and find a recurrence relation? Or in other words, something that would be easier for a computer to understand (let's say I wanted to write a program which can take a series of numbers and then compute the relation automatically)
$a\_n=...$