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A203477 a(n) = Product_{0 <= i < j <= n-1} (2^i + 2^j).

%I A203477 #23 Aug 28 2023 03:35:02
%S A203477 1,3,90,97200,14276736000,1107198567383040000,
%T A203477 178601637561927097909248000000,
%U A203477 237856509917156074017606774172522905600000000,10420480393274493153643458442091600404477248333907230720000000000
%N A203477 a(n) = Product_{0 <= i < j <= n-1} (2^i + 2^j).
%C A203477 Each term divides its successor, as in A203478.
%H A203477 G. C. Greubel, <a href="/A203477/b203477.txt">Table of n, a(n) for n = 1..21</a>
%p A203477 a:= n-> mul(mul(2^i+2^j, i=0..j-1), j=1..n-1):
%p A203477 seq(a(n), n=1..10);  # _Alois P. Heinz_, Jul 23 2017
%t A203477 (* First program *)
%t A203477 f[j_]:= 2^(j-1); z = 13;
%t A203477 v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
%t A203477 Table[v[n], {n,z}]                       (* A203477 *)
%t A203477 Table[v[n+1]/v[n], {n,z-1}]              (* A203478 *)
%t A203477 Table[v[n]*v[n+2]/(2*v[n+1]^2), {n,22}]  (* A164051 *)
%t A203477 (* Second program *)
%t A203477 Table[Product[(2^j^2)*QPochhammer[-1/2^j,2,j], {j,0,n-1}], {n,20}] (* _G. C. Greubel_, Aug 28 2023 *)
%o A203477 (PARI) a(n)=prod(i=0,n-2,prod(j=i+1,n-1,2^i+2^j)) \\ _Charles R Greathouse IV_, Feb 16 2021
%o A203477 (Magma) [(&*[(&*[2^j + 2^k: k in [0..j]])/2^(j+1): j in [0..n-1]]): n in [1..20]]; // _G. C. Greubel_, Aug 28 2023
%o A203477 (SageMath) [product(product(2^j + 2^k for k in range(j)) for j in range(n)) for n in range(1,21)] # _G. C. Greubel_, Aug 28 2023
%Y A203477 Cf. A000079, A093883, A164051, A203305, A203478.
%K A203477 nonn,easy
%O A203477 1,2
%A A203477 _Clark Kimberling_, Jan 02 2012
%E A203477 Name edited by _Alois P. Heinz_, Jul 23 2017