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%I #13 Dec 17 2014 21:12:20
%S 1,5,1700,601120000,3496121614336000000,
%T 5335507266769461885009920000000000,
%U 34161019296423817239835748940949012820787200000000000000
%N Vandermonde sequence using x^2 + y^2 applied to (1,2,4,...,2^(n-1)).
%C See A093883 for a discussion and guide to related sequences.
%H Todd Silvestri, <a href="/A203683/b203683.txt">Table of n, a(n) for n = 1..17</a>
%F a(n) = product(((5*4^(k*(k+1)))/(4^(k+1)+1))*(-4^-(k+1);4)_k, k = 1..n-1), where the q-Pochhammer symbol (c;q)_m = product(1-c*q^j, j = 0..m-1). - _Todd Silvestri_, Dec 15 2014
%t f[j_] := 2^(j - 1); z = 12;
%t u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
%t v[n_] := Product[u[n], {k, 2, n}]
%t Table[v[n], {n, 1, z}] (* A203683 *)
%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203684 *)
%t a[n_Integer/;n>=1]:=Product[(5 4^(k (k+1)))/(4^(k+1)+1) QPochhammer[-4^-(k+1),4,k],{k,n-1}] (* _Todd Silvestri_, Dec 15 2014 *)
%K nonn
%O 1,2
%A _Clark Kimberling_, Jan 04 2012
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