By Doron Zeilberger
To have the computer guess, and (rigorously prove at the same time!) the recurrence for the
Dyson product for n from 2 to 8, the
input
gives the
output.
You don't have to be Jack Good to be able to conjecture that this holds for all n,
and then prove it for all n (Good did it with the Lagrange interpolation formula).