|
%I #16 Dec 08 2023 04:54:12
%S 1,2,1081600,528465082730906880000,
%T 29276520893554373473343522853366005760000000000,
%U 5719545329208791496596894540018824083491259163047733746620041978183680000000000000000
%N a(n) = Product_{i=1..n, j=1..n} (i^6 + j^6).
%F a(n) ~ c * 2^(n*(n+1)) * (2 + sqrt(3))^(sqrt(3)*n*(n+1)) * exp(Pi*n*(n+1) - 9*n^2) * n^(6*n^2 - 3/2), where c = 0.104143806044091748191387307161835081649...
%F a(n) = A324403(n) * A367668(n). - _Vaclav Kotesovec_, Dec 01 2023
%F For n>0, a(n)/a(n-1) = A367823^2 / (2*n^18). - _Vaclav Kotesovec_, Dec 02 2023
%p a:= n-> mul(mul(i^6 + j^6, i=1..n), j=1..n):
%p seq(a(n), n=0..5); # _Alois P. Heinz_, Nov 26 2023
%t Table[Product[i^6 + j^6, {i, 1, n}, {j, 1, n}], {n, 1, 6}]
%o (Python)
%o from math import prod, factorial
%o def A324439(n): return (prod(i**6+j**6 for i in range(1,n) for j in range(i+1,n+1))*factorial(n)**3)**2<<n # _Chai Wah Wu_, Nov 26 2023
%Y Cf. A079478, A324403, A324426, A324437, A324438, A324440, A367834.
%Y Cf. A367668, A367823.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Feb 28 2019
%E a(n)=1 prepended by _Alois P. Heinz_, Nov 26 2023
|
