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%I A324437 #22 Dec 08 2023 04:52:53
%S A324437 1,2,18496,189567553208832,53863903330477722171391434817536,
%T A324437 4194051697335929481600368256016484482740174637152337920000,
%U A324437 530545265060440849231458462212366841894726534233233018777709463062563850450708386692464640000
%N A324437 a(n) = Product_{i=1..n, j=1..n} (i^4 + j^4).
%F A324437 a(n) ~ c * 2^(n*(n+1)) * exp(Pi*n*(n+1)/sqrt(2) - 6*n^2) * (1 + sqrt(2))^(sqrt(2)*n*(n+1)) * n^(4*n^2 - 1), where c = A306620 = 0.23451584451404279281807143317500518660696293944961...
%F A324437 For n>0, a(n)/a(n-1) = A272247(n)^2 / (2*n^12). - _Vaclav Kotesovec_, Dec 01 2023
%p A324437 a:= n-> mul(mul(i^4+j^4, i=1..n), j=1..n):
%p A324437 seq(a(n), n=0..7);  # _Alois P. Heinz_, Jun 24 2023
%t A324437 Table[Product[i^4 + j^4, {i, 1, n}, {j, 1, n}], {n, 1, 6}]
%o A324437 (Python)
%o A324437 from math import prod, factorial
%o A324437 def A324437(n): return (prod(i**4+j**4 for i in range(1,n) for j in range(i+1,n+1))*factorial(n)**2)**2<<n # _Chai Wah Wu_, Nov 26 2023
%Y A324437 Cf. A079478, A324403, A324426, A324438, A324439, A324440, A367834.
%Y A324437 Cf. A203677, A272247, A307215.
%K A324437 nonn
%O A324437 0,2
%A A324437 _Vaclav Kotesovec_, Feb 28 2019
%E A324437 a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2023

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