A324444 a(n) = Product_{i=1..n, j=1..n} (1 + i + j).

1, 3, 240, 1512000, 1536288768000, 429266120461516800000, 50406068004584362019389440000000, 3534677027377560888380072035048488960000000000, 199761495428405897006583857561824669625759249203200000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..8.

Formula

a(n) ~ A * 2^(2*n^2 + 4*n + 11/12) * n^(n^2 - 23/12) / (Pi * exp(3*n^2/2 + 1/12)), where A is the Glaisher-Kinkelin constant A074962.

a(n) = BarnesG(2*n + 3) / BarnesG(n + 3)^2.

Product_{i=1..n, j=1..n} (1 + 1/(i + j)) = a(n) / A079478(n) ~ 2^(2*n + 1) / (sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 29 2019

Maple

a:= n-> mul(mul(i+j+1, i=1..n), j=1..n):
seq(a(n), n=0..9);  # Alois P. Heinz, Jun 24 2023

Mathematica

Table[Product[1 + i + j, {i, 1, n}, {j, 1, n}], {n, 1, 10}]
Table[BarnesG[2*n + 3] / BarnesG[n + 3]^2, {n, 1, 10}]

Prog

(PARI) a(n) = prod(i=1, n, prod(j=1, n, 1+i+j)); \\ Michel Marcus, Feb 28 2019
(Magma) [(&*[(&*[1+k+j: j in [1..n]]): k in [1..n]]): n in [1..10]]; // G. C. Greubel, Feb 28 2019
(Sage) [product( product(1+k+j for j in (1..n)) for k in (1..n)) for n in (1..10)] # G. C. Greubel, Feb 28 2019

Crossrefs

Cf. A079478, A306594.

Sequence in context: A024044 A356568 A069640 * A236249 A338453 A013778

Adjacent sequences: A324441 A324442 A324443 * A324445 A324446 A324447

Keyword

nonn

Author

Vaclav Kotesovec, Feb 28 2019

Extensions

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

Status

approved