cp's OEIS Frontend

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.

A367670 a(n) = Product_{i=1..n, j=1..n} (i^8 + i^4*j^4 + j^8).

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%I A367670 #8 Nov 26 2023 12:58:10
%S A367670 3,171714816,9817265089769041882465383168,
%T A367670 351690857158733335833718073682368165890982417955022627663773696
%N A367670 a(n) = Product_{i=1..n, j=1..n} (i^8 + i^4*j^4 + j^8).
%F A367670 a(n) = A367550(n) * A367668(n).
%F A367670 a(n) = A367542(n) * A367543(n) * A367668(n).
%F A367670 a(n) ~ c * 3^(3*n*(n+1)/2) * (2 + sqrt(3))^(sqrt(3)*n*(n+1)) * n^(8*n^2 - 2) / exp(12*n^2 - Pi*(1 + sqrt(3))*n*(n+1)/2), where c = 0.05091893538977858024246640150391280389386566805866250210433631511020673755...
%t A367670 Table[Product[Product[i^8 + i^4*j^4 + j^8, {i, 1, n}], {j, 1, n}], {n, 1, 7}]
%o A367670 (Python)
%o A367670 from math import prod, factorial
%o A367670 def A367670(n): return (prod((k:=j**4)**2+(m:=i**4)*(m+k) for i in range(1,n) for j in range(i+1,n+1))*factorial(n)**4)**2*3**n # _Chai Wah Wu_, Nov 26 2023
%Y A367670 Cf. A367542, A367543, A367550, A367668.
%K A367670 nonn
%O A367670 1,1
%A A367670 _Vaclav Kotesovec_, Nov 26 2023