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b[s_, k_] := b[s, k] = With[{n = Length[s]}, If[n == 0, 1, Sum[
If[Abs[i-n] == k, 0, b[s ~Complement~ {i}, k]], {i, s}]]];
A[n_, k_] := If[k >= n, n!, b[Range@n, k]];
Table[A[n, d-n], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, Sep 01 2021, from second Maple program *)
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Table[A[n, d-n], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 05 2021, from first Maple program *)
Maple program *)
A[n_, k_] := If[k > n, n!, Permanent[Table[If[Abs[i-j] == k, 0, 1], {i, 1, n}, {j, 1, n}]]]; A[0, 0] = 1;
Table[A[n, d-n], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 05 2021, from first
Maple program *)
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