Rational numbers recurrence

"Rational numbers recurrence"

(*start*)
(*Mathematica*)
Clear[t]
c = 2
nn = 12;
t[n_, 1] = If[n >= 1, n, n];
t[n_, k_] :=
  t[n, k] =
    If[n > k,
      Sum[t[(n - i), k - 1], {i, 1, c*(k - 1)}] -
        Sum[t[(n - i), k], {i, 1, c*(k - 1) + 1}], n/k]
TableForm[Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}]]
TableForm[Table[Table[t[n, k] - n/k, {k, 1, nn}], {n, 1, nn}]]
(*end*)