This is a No-rectangles Fillomino puzzle. In addition to the usual rules, none of the polyominoes can form a rectangle.
Answer Entry: Enter the units digits (last digit) of the number in each circled cell starting with the leftmost column and going right.
Highlight to see answer: 47656765
EDIT: I meant to point out originally that this puzzle was the inspiration. (That’s the second time this blog has linked to that puzzle.)