A368622 a(n) = Product_{j=1..n, k=1..n} (j^2 + k^2 + n^2).

1, 3, 5832, 172907569296, 419358815743567702818816, 267800543010963952830647446563000000000000, 110831581527076064529150462985910455129725821244148698662830080000

Offset: 0

Author

Vaclav Kotesovec, Jan 01 2024

Keywords

• nonn

Comments

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.

Crossrefs

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

Programs

Mathematica

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

Formula

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...