This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324403 #38 Jul 01 2025 01:07:25
%S A324403 1,2,400,121680000,281324160000000000,
%T A324403 15539794609114833408000000000000,
%U A324403 49933566483104048708063697937367040000000000000000,19323883089768863178599626514889213871887405416448000000000000000000000000
%N A324403 a(n) = Product_{i=1..n, j=1..n} (i^2 + j^2).
%C A324403 Next term is too long to be included.
%F A324403 a(n) ~ 2^(n*(n+1) - 3/4) * exp(Pi*n*(n+1)/2 - 3*n^2 + Pi/12) * n^(2*n^2 - 1/2) / (Pi^(1/4) * Gamma(3/4)).
%F A324403 a(n) = 2*n^2*a(n-1)*Product_{i=1..n-1} (n^2 + i^2)^2. - _Chai Wah Wu_, Feb 26 2019
%F A324403 For n>0, a(n)/a(n-1) = A272244(n)^2 / (2*n^6). - _Vaclav Kotesovec_, Dec 02 2023
%F A324403 a(n) = exp(2*Integral_{x=0..oo} (n^2/(x*exp(x)) - (cosh(n*x) - cos(n*x))/(x*exp((n + 1)*x)*(cosh(x) - cos(x)))) dx)/2^(n^2). - _Velin Yanev_, Jun 30 2025
%p A324403 a:= n-> mul(mul(i^2+j^2, i=1..n), j=1..n):
%p A324403 seq(a(n), n=0..7); # _Alois P. Heinz_, Jun 24 2023
%t A324403 Table[Product[i^2+j^2, {i, 1, n}, {j, 1, n}], {n, 1, 10}]
%o A324403 (PARI) a(n) = prod(i=1, n, prod(j=1, n, i^2+j^2)); \\ _Michel Marcus_, Feb 27 2019
%o A324403 (Python)
%o A324403 from math import prod, factorial
%o A324403 def A324403(n): return (prod(i**2+j**2 for i in range(1,n) for j in range(i+1,n+1))*factorial(n))**2<<n # _Chai Wah Wu_, Nov 22 2023
%Y A324403 Cf. A079478, A324426, A324437, A324438, A324439, A324440, A367834.
%Y A324403 Cf. A272244, A293290, A324402, A324443, A324425.
%K A324403 nonn
%O A324403 0,2
%A A324403 _Vaclav Kotesovec_, Feb 26 2019
%E A324403 a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2023