A368622 - OEIS

%I #8 Jan 06 2024 14:24:57

%S 1,3,5832,172907569296,419358815743567702818816,

%T 267800543010963952830647446563000000000000,

%U 110831581527076064529150462985910455129725821244148698662830080000

%N a(n) = Product_{j=1..n, k=1..n} (j^2 + k^2 + n^2).

%C The limit has a closed form. In Mathematica: Exp[Integrate[Log[x^2 + y^2 + 1], {x,0,1}, {y,0,1}]]. The output is extremely large.

%F Limit_{n->oo} a(n)^(1/(n^2)) / n^2 = exp(Integral_{x=0..1, y=0..1} log(x^2 + y^2 + 1) dy dx) = 1.6143980185761253961882683158432481977126507900460725431661...

%t Table[Product[j^2 + k^2 + n^2, {j, 1, n}, {k, 1, n}], {n, 0, 10}]

%Y Cf. A272244, A324403, A324425, A368720, A368721.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 01 2024