Here we go… 

1 x 2 x 3 x 4 = 24 = 5² – 1

2 x 3 x 4 x 5 = 120 = 11² – 1

3 x 4 x 5 x 6 = 360 = 19² – 1

Golly! Is every product of four consecutive integers one less than a perfect square??