Mathematica 8

Clear[t, A, B]

nn = 16;

A = Table[Table[If[n >= k, 1, 0], {k, 1, nn}], {n, 1, nn}];

MatrixForm[A];

B = A;

Do[

Clear[t, A];

t[n_, k_] :=

t[n, k] =

If[k == 1, If[Mod[n, j] == 1, 1, 0],

If[n >= k, t[n - 1, k - 1], 0]];

A = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];

B = B.A;

(*Print[MatrixForm[B]]*)

, {j, 2, nn}]

B[[All, 1]]

{1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176}

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