Question 26380
If n=1, 1^2=1 (1-1)! is meaningless
If n=2, 2^2=4 (2-1)!=1 ;2 does not meet the criteria
If n=3, 3^3=9 (3-1)!=2 ;3 does not meet the criteria
If n=5, 5^2=25 4!=24 does not meet criteria
If n=6, 6^2=36 (6-1)!=120 meets the criteria
Ifn=7, 7^2=49 6!=720 meets the criteria
Looks like all n>5 meet the criteria

Cheers,
Stan H.