cp's OEIS Frontend

A203479 a(n) = Product_{1 <= i < j <= n} (2^i + 2^j - 2).

%I A203479 #19 Aug 09 2025 07:07:51
%S A203479 1,4,320,2027520,3855986196480,8359491805553413324800,
%T A203479 79457890145647634305213865656320000,
%U A203479 12897878211365028383150895090566532213003150950400000,140613650417826346093374124598539442743630963394643403845144815232614400000
%N A203479 a(n) = Product_{1 <= i < j <= n} (2^i + 2^j - 2).
%C A203479 Each term divides its successor, as in A203480.
%H A203479 G. C. Greubel, <a href="/A203479/b203479.txt">Table of n, a(n) for n = 1..21</a>
%F A203479 a(n) ~ c * 2^((n-1)*n*(n+1)/3) / QPochhammer(1/2, 1/4)^(n-1), where c = 0.0732262905669624786298393270254722268761908164083517721484477901776137... - _Vaclav Kotesovec_, Aug 09 2025
%p A203479 a:= n-> mul(mul(2^i+2^j-2, i=1..j-1), j=2..n):
%p A203479 seq(a(n), n=1..12);  # _Alois P. Heinz_, Jul 23 2017
%t A203479 (* First program *)
%t A203479 f[j_]:= 2^j -1; z = 15;
%t A203479 v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
%t A203479 Table[v[n], {n,z}]               (* A203479 *)
%t A203479 Table[v[n+1]/v[n], {n,z-1}]      (* A203480 *)
%t A203479 Table[v[n+1]/(4*v[n]), {n,z-1}]  (* A203481 *)
%t A203479 (* Second program *)
%t A203479 Table[Product[2^j +2^k -2, {j,n}, {k,j-1}], {n,15}] (* _G. C. Greubel_, Aug 28 2023 *)
%o A203479 (Magma) [(&*[(&*[2^j+2^k-2: k in [1..j]])/(2^(j+1)-2): j in [1..n]]): n in [1..15]]; // _G. C. Greubel_, Aug 28 2023
%o A203479 (SageMath) [product(product(2^j+2^k-2 for k in range(1,j)) for j in range(1,n+1)) for n in range(1,16)] # _G. C. Greubel_, Aug 28 2023
%Y A203479 Cf. A000225, A093883, A203305, A203480, A203481.
%K A203479 nonn
%O A203479 1,2
%A A203479 _Clark Kimberling_, Jan 02 2012
%E A203479 Name edited by _Alois P. Heinz_, Jul 23 2017