cp's OEIS Frontend

A324427 a(n) = Product_{k=1..n} (Product_{j=1..k} (Product_{i=1..j} (i+j+k))).

%I A324427 #15 Nov 27 2023 05:06:15
%S A324427 1,3,360,38102400,109506663383040000,
%T A324427 337878174593229551661219840000000,
%U A324427 54048023654871725380569225530796717972337459200000000000,25571582464158460440549345359703385621119611033206432205259362823202406400000000000000000
%N A324427 a(n) = Product_{k=1..n} (Product_{j=1..k} (Product_{i=1..j} (i+j+k))).
%F A324427 a(n) ~ 3^(3*n^3/4 + 9*n^2/4 + 47*n/24 + 7/24) * n^(n^3/6 + n^2/2 + n/3) / (2^(2*n^3/3 + 2*n^2 + 7*n/4 + 7/24) * exp(11*n^3/36 + 3*n^2/4 + n/3 - zeta(3)/(48*Pi^2))). - _Vaclav Kotesovec_, Nov 27 2023
%p A324427 a:= n-> mul(mul(mul(i+j+k, i=1..j), j=1..k), k=1..n):
%p A324427 seq(a(n), n=0..8);  # _Alois P. Heinz_, Jun 24 2023
%t A324427 Table[Product[Product[Product[i+j+k, {i, 1, j}], {j, 1, k}], {k, 1, n}], {n, 0, 10}]
%t A324427 Table[Sqrt[Product[2^k Gamma[1 + 3*k/2]/Gamma[1 + k/2] (BarnesG[2 + k] BarnesG[2 + 3 k] )/BarnesG[2 + 2 k]^2 , {k, 1, n}]], {n, 0, 10}]
%o A324427 (PARI) a(n) = prod(k=1, n, prod(j=1, k, prod(i=1, j, i+j+k))); \\ _Michel Marcus_, Feb 27 2019
%Y A324427 Cf. A079478, A112332, A306594.
%K A324427 nonn
%O A324427 0,2
%A A324427 _Vaclav Kotesovec_, Feb 27 2019
%E A324427 a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2023