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For some reason, falling_factorial is expecting Sage's integers (Integer), not Python's ones (int). So replace range(6) by (0..5) in your command and it will work:

sage: for n in (0..5): [falling_factorial(n, n-k-1) for k in (0..n)]
[1]
[1, 1/2]
[2, 1, 1/3]
[6, 3, 1, 1/4]
[24, 12, 4, 1, 1/5]
[120, 60, 20, 5, 1, 1/6]