Hey Katekadah.

It could literally be any number of sequences but each successive difference has a difference of n! The sequence {8,10,16} when looked at in terms of differences is {2!,3!} so if you apply this pattern then you get a difference of (2!,3!,4!,5!,6!,7!} which means the final number if 2! + 3! + 4! + 5! + 6! + 7! using this specific pattern.

Remember that you can have potentially infinite numbers of sequences just like you can have infinite numbers of polynomials with specific roots.