The sequence gives the number of distinct tilings by polyominoes of a square with side n. As for "free" polyominoes, tilings that are reflections or rotations of each other are not considered distinct.

Using the same terminology used for polyominoes: the corresponding sequence for "fixed" tilings is 1,12,1434,1691690, and for one-sided tilings is 1,5,222,213315.

Cf. A268416 (polyominoes that will fit in n-sided square), A291807 (symmetric tilings), A291808 (tilings with distinct polyominoes), A291809 (tilings with differently sized polyominoes).