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A203480 a(n) = v(n+1)/v(n), where v = A203479.

%I A203480 #17 Aug 09 2025 06:38:16
%S A203480 4,80,6336,1901824,2167925760,9505110118400,162323441859870720,
%T A203480 10902076148767162433536,2898720791385603198124032000,
%U A203480 3064112360434477703904869089280000,12909951234577776926559241120412860416000
%N A203480 a(n) = v(n+1)/v(n), where v = A203479.
%H A203480 G. C. Greubel, <a href="/A203480/b203480.txt">Table of n, a(n) for n = 1..55</a>
%F A203480 a(n) = Product_{k=1..n} (2^k + 2^(n+1) - 2). - _G. C. Greubel_, Aug 28 2023
%F A203480 a(n) ~ c * 2^(n*(n+1)), where c = 1/QPochhammer(1/2, 1/4) = A079555 = 2.3842310290313717... - _Vaclav Kotesovec_, Aug 09 2025
%t A203480 (* First program *)
%t A203480 f[j_]:= 2^j - 1; z = 15;
%t A203480 v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
%t A203480 Table[v[n], {n,z}]               (* A203479 *)
%t A203480 Table[v[n+1]/v[n], {n,z-1}]      (* A203480 *)
%t A203480 Table[v[n+1]/(4*v[n]), {n,z-1}]  (* A203481 *)
%t A203480 (* Second program *)
%t A203480 Table[Product[2^(n+1) +2^k -2, {k,n}], {n,20}] (* _G. C. Greubel_, Aug 28 2023 *)
%o A203480 (Magma) [(&*[2^j +2^(n+1) -2: j in [1..n]]): n in [1..20]]; // _G. C. Greubel_, Aug 28 2023
%o A203480 (SageMath) [product(2^j+2^(n+1)-2 for j in range(1,n+1)) for n in range(1,21)] # _G. C. Greubel_, Aug 28 2023
%Y A203480 Cf. A093883, A203307, A203479.
%Y A203480 Cf. A079555.
%K A203480 nonn
%O A203480 1,1
%A A203480 _Clark Kimberling_, Jan 02 2012