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A203478 a(n) = v(n+1)/v(n), where v = A203477.

%I A203478 #22 Aug 28 2023 03:27:43
%S A203478 3,30,1080,146880,77552640,161309491200,1331771159347200,
%T A203478 43809944057885491200,5753472333233985788313600,
%U A203478 3019422280481195741706977280000,6335279362770913356551778761441280000
%N A203478 a(n) = v(n+1)/v(n), where v = A203477.
%H A203478 G. C. Greubel, <a href="/A203478/b203478.txt">Table of n, a(n) for n = 1..55</a>
%F A203478 a(n) = A028362(n+1) * 2^(n*(n-1)/2). - _Charles R Greathouse IV_, Feb 16 2021
%F A203478 a(n) = Product_{j=0..n-1} (2^j + 2^n). - _G. C. Greubel_, Aug 28 2023
%t A203478 (* First program *)
%t A203478 f[j_]:= 2^(j-1); z = 13;
%t A203478 v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
%t A203478 Table[v[n], {n,z}]                       (* A203477 *)
%t A203478 Table[v[n+1]/v[n], {n,z-1}]              (* A203478 *)
%t A203478 Table[v[n]*v[n+2]/(2*v[n+1]^2), {n,22}]  (* A164051 *)
%t A203478 (* Second program *)
%t A203478 Table[Product[2^j +2^n, {j,0,n-1}], {n,20}] (* _G. C. Greubel_, Aug 28 2023 *)
%o A203478 (PARI) a(n)=prod(i=0,n-1,2^i+2^n) \\ _Charles R Greathouse IV_, Feb 16 2021
%o A203478 (Magma) [(&*[2^j + 2^n: j in [0..n-1]]): n in [1..20]]; // _G. C. Greubel_, Aug 28 2023
%o A203478 (SageMath) [product(2^j + 2^n for j in range(n)) for n in range(1,21)] # _G. C. Greubel_, Aug 28 2023
%Y A203478 Cf. A028362, A093883, A164051, A203307, A203477.
%K A203478 nonn,easy
%O A203478 1,1
%A A203478 _Clark Kimberling_, Jan 02 2012