Is this graphing calculator broken, or is this someting really weird?

Question

The function is $y=x!-(\text{floor}(\sqrt{x!})^2-1)$, with $\text{floor}(x!)$ being the floor function of $x!$

Answer 1

This generates the sequence $$\{1,1,2,3,9,21,45,141,321,477,3585,12312,4605,74880,414120,2071776,5703552,\cdots \}$$

For the sequence $$a_n=n!-\left\lfloor \sqrt{n!}\right\rfloor ^2$$ have a look at sequence $A066857$ in $OEIS$.