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A203481 a(n) = v(n+1)/(4*v(n)), where v = A203479.

%I A203481 #15 Aug 09 2025 06:42:01
%S A203481 1,20,1584,475456,541981440,2376277529600,40580860464967680,
%T A203481 2725519037191790608384,724680197846400799531008000,
%U A203481 766028090108619425976217272320000,3227487808644444231639810280103215104000
%N A203481 a(n) = v(n+1)/(4*v(n)), where v = A203479.
%H A203481 G. C. Greubel, <a href="/A203481/b203481.txt">Table of n, a(n) for n = 1..55</a>
%F A203481 a(n) = (1/4)*Product_{k=1..n} (2^k + 2^(n+1) - 2). - _G. C. Greubel_, Aug 28 2023
%F A203481 a(n) ~ c * 2^(n*(n+1)-2), where c = 1/QPochhammer(1/2, 1/4) = A079555 = 2.3842310290313717... - _Vaclav Kotesovec_, Aug 09 2025
%t A203481 (* First program *)
%t A203481 f[j_]:= 2^j - 1; z = 15;
%t A203481 v[n_]:= Product[Product[f[k] + f[j], {j, k-1}], {k, 2, n}]
%t A203481 Table[v[n], {n, z}]               (* A203479 *)
%t A203481 Table[v[n+1]/v[n], {n, z-1}]      (* A203480 *)
%t A203481 Table[v[n+1]/(4*v[n]), {n, z-1}]  (* A203481 *)
%t A203481 (* Second program *)
%t A203481 Table[Product[2^(n+1) +2^k -2, {k,n}]/4, {n,20}] (* _G. C. Greubel_, Aug 28 2023 *)
%o A203481 (Magma) [(&*[2^j + 2^(n+1) - 2: j in [1..n]])/4: n in [1..20]]; // _G. C. Greubel_, Aug 28 2023
%o A203481 (SageMath) [product(2^j+2^(n+1)-2 for j in range(1,n+1))/4 for n in range(1,21)] # _G. C. Greubel_, Aug 28 2023
%Y A203481 Cf. A203479, A203480, A093883.
%Y A203481 Cf. A079555.
%K A203481 nonn
%O A203481 1,2
%A A203481 _Clark Kimberling_, Jan 02 2012