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Mathematica:

Table[FactorialPower[n, n - k - 1], {n, 0, 5}, {k, 0, n}]
{{1}, {1, 1/2}, {2, 1, 1/3}, {6, 3, 1, 1/4}, {24, 12, 4, 1, 1/5}}

• Maple:

  ff := (n,k) -> n!/(n-k)!:
  for n from 0 to 5 do seq(ff(n, n-k-1), k=0..n) od;
              1
            1, 1/2
          2, 1, 1/3
        6, 3, 1, 1/4
      24, 12, 4, 1, 1/5
  

• Sage:

   for n in range(6): [falling_factorial(n, n-k-1) for k in (0..n)]
   AttributeError: 'int' object has no attribute 'parent'