Crazy sequence

[rocdocmac 9]

Perhaps you've seen this one before, but I've added an extra twist to it!

 

    What are the next two entries in this sequence?

 

All credit due to the original designer from whom I've borrowed it (source to be disclosed once question is answered).

Edited May 1 by rocdocmac
wording

[Thalia 64]

(((((((8!)!)!)!)!)!)!)!

((((((((((((13!)!)!)!)!)!)!)!)!)!)!)!)!

[rocdocmac 9]

Hint ...

Spoiler

720 = 6!

 

[rocdocmac 9]

@Thalia ..

Spoiler

Very well done!

 

[bonanova 83]

Spoiler

filius Bonacci lives ...