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FORMULA
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a(n) = ((5*4^(n*(n+1)))/(4^(n+1)+1))*(-4^-(n+1);4)_n, where the q-Pochhammer symbol (c;q)_m = product(1-c*q^j, j = 0..m-1). - Todd Silvestri, Nov 16 2014
a(n+1) = (4^n + 4^(2*n+1))*a(n). - Robert Israel, Dec 15 2014
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MATHEMATICA
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f[j_] := 2^(j - 1); z = 12;
u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}] (* A203683 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203684 *)
a[n_Integer/; n>=1]:=(5 4^(n (n+1)))/(4^(n+1)+1) QPochhammer[-4^-(n+1), 4, n] (* Todd Silvestri, Nov 16 2014 *)
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