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A203307 a(n) = v(n+1)/(2*v(n)), where v = A203305.

%I A203307 #11 Aug 31 2023 02:56:20
%S A203307 1,12,672,161280,159989760,645078712320,10486399547473920,
%T A203307 684552162459097497600,179100751368498596492083200,
%U A203307 187617350297573441752474740326400,786539962489104046627462744981792358400
%N A203307 a(n) = v(n+1)/(2*v(n)), where v = A203305.
%H A203307 G. C. Greubel, <a href="/A203307/b203307.txt">Table of n, a(n) for n = 1..50</a>
%F A203307 a(n) = (1/2)*A028365(n) for n>0.
%F A203307 a(n) = (-1)^n * 2^(binomial(n+1,2) - 1) * QPochhammer(2,2,n). - _G. C. Greubel_, Aug 31 2023
%t A203307 (* First program *)
%t A203307 f[j_]:= 2^j - 1; z = 15;
%t A203307 v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
%t A203307 Table[v[n], {n,z}]         (* A203305 *)
%t A203307 Table[v[n+1]/v[n], {n,z}]  (* A028365 *)
%t A203307 %/2                         (* A203307 *)
%t A203307 (* Second program *)
%t A203307 Table[(-1)^n*2^Binomial[n+1,2]*QPochhammer[2,2,n]/2, {n,20}] (* _G. C. Greubel_, Aug 31 2023 *)
%o A203307 (Magma) [(&*[2^(n+1) - 2^(j+1): j in [0..n-1]])/2: n in [1..20]]; // _G. C. Greubel_, Aug 31 2023
%o A203307 (SageMath) [product(2^(n+1) - 2^(k+1) for k in range(n))/2 for n in range(1,21)] # _G. C. Greubel_, Aug 31 2023
%Y A203307 Cf. A203305, A028365.
%K A203307 nonn
%O A203307 1,2
%A A203307 _Clark Kimberling_, Jan 01 2012