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A203475 a(n) = Product_{1 <= i < j <= n} (i^2 + j^2).

%I A203475 #30 Nov 22 2023 04:50:53
%S A203475 1,5,650,5525000,5807194900000,1226800120038480000000,
%T A203475 77092420109247492627600000000000,
%U A203475 2001314057760220784660590245696000000000000000,28468550112906756205383102673584071297339520000000000000000000
%N A203475 a(n) = Product_{1 <= i < j <= n} (i^2 + j^2).
%C A203475 Each term divides its successor, as in A203476.
%H A203475 G. C. Greubel, <a href="/A203475/b203475.txt">Table of n, a(n) for n = 1..28</a>
%F A203475 a(n) ~ c * 2^(n^2/2) * exp(Pi*n*(n+1)/4 - 3*n^2/2 + n) * n^(n*(n-1) - 3/4), where c = A323755 = sqrt(Gamma(1/4)) * exp(Pi/24) / (2*Pi)^(9/8) = 0.274528350333552903800408993482507428142383783773190451181... - _Vaclav Kotesovec_, Jan 26 2019
%p A203475 a:= n-> mul(mul(i^2+j^2, i=1..j-1), j=2..n):
%p A203475 seq(a(n), n=1..10);  # _Alois P. Heinz_, Jul 23 2017
%t A203475 f[j_]:= j^2; z = 15;
%t A203475 v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
%t A203475 Table[v[n], {n,z}]           (* A203475 *)
%t A203475 Table[v[n+1]/v[n], {n,z-1}]  (* A203476 *)
%o A203475 (Magma) [(&*[(&*[j^2 + k^2: k in [1..j]])/(2*j^2): j in [1..n]]): n in [1..20]]; // _G. C. Greubel_, Aug 28 2023
%o A203475 (SageMath) [product(product(j^2+k^2 for k in range(1,j)) for j in range(1,n+1)) for n in range(1,21)] # _G. C. Greubel_, Aug 28 2023
%Y A203475 Cf. A000290, A093883, A202768, A203476, A272244, A293290, A323755, A324403, A367517.
%K A203475 nonn
%O A203475 1,2
%A A203475 _Clark Kimberling_, Jan 02 2012
%E A203475 Name edited by _Alois P. Heinz_, Jul 23 2017