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MATHEMATICA
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f[j_] := 2^(j - 1); z = 13;
v[n_] := Product[Product[f[k] + f[j],
{j, 1, k - 1}], {k, 2, n}]
Table[v[n], {n, 1, z}] (* A203477 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203478 *)
Table[v[n] v[n + 2]/(2*v[n + 1]^2),
{n, 1, 22}] (* A164051 *)
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