This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324444 #17 Jun 24 2023 16:39:24 %S A324444 1,3,240,1512000,1536288768000,429266120461516800000, %T A324444 50406068004584362019389440000000, %U A324444 3534677027377560888380072035048488960000000000,199761495428405897006583857561824669625759249203200000000000000 %N A324444 a(n) = Product_{i=1..n, j=1..n} (1 + i + j). %F A324444 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. %F A324444 a(n) = BarnesG(2*n + 3) / BarnesG(n + 3)^2. %F A324444 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 %p A324444 a:= n-> mul(mul(i+j+1, i=1..n), j=1..n): %p A324444 seq(a(n), n=0..9); # _Alois P. Heinz_, Jun 24 2023 %t A324444 Table[Product[1 + i + j, {i, 1, n}, {j, 1, n}], {n, 1, 10}] %t A324444 Table[BarnesG[2*n + 3] / BarnesG[n + 3]^2, {n, 1, 10}] %o A324444 (PARI) a(n) = prod(i=1, n, prod(j=1, n, 1+i+j)); \\ _Michel Marcus_, Feb 28 2019 %o A324444 (Magma) [(&*[(&*[1+k+j: j in [1..n]]): k in [1..n]]): n in [1..10]]; // _G. C. Greubel_, Feb 28 2019 %o A324444 (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 %Y A324444 Cf. A079478, A306594. %K A324444 nonn %O A324444 0,2 %A A324444 _Vaclav Kotesovec_, Feb 28 2019 %E A324444 a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2023