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

1, 3, 360, 38102400, 109506663383040000, 337878174593229551661219840000000, 54048023654871725380569225530796717972337459200000000000, 25571582464158460440549345359703385621119611033206432205259362823202406400000000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Formula

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

Maple

a:= n-> mul(mul(mul(i+j+k, i=1..j), j=1..k), k=1..n):
seq(a(n), n=0..8);  # Alois P. Heinz, Jun 24 2023

Mathematica

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

Prog

(PARI) a(n) = prod(k=1, n, prod(j=1, k, prod(i=1, j, i+j+k))); \\ Michel Marcus, Feb 27 2019

Crossrefs

Cf. A079478, A112332, A306594.

Sequence in context: A297483 A355753 A324402 * A304285 A324269 A173648

Adjacent sequences: A324424 A324425 A324426 * A324428 A324429 A324430

Keyword

nonn

Author

Vaclav Kotesovec, Feb 27 2019

Extensions

a(0)=1 prepended by Alois P. Heinz, Jun 24 2023

Status

approved