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a(n) = Product_{i=1..n, j=1..n} (2*i + j).
6

%I #21 Dec 10 2023 09:04:28

%S 1,3,360,6350400,36212520960000,117563342374788710400000,

%T 337905477880065368190647009280000000,

%U 1234818479230749311108497004714406224855040000000000,7795494015765035913020359514023640290443493305037073940480000000000000

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

%H Robert Israel, <a href="/A324402/b324402.txt">Table of n, a(n) for n = 0..25</a>

%F a(n) ~ sqrt(A/Pi) * 3^(9*n*(n+1)/4 + 11/24) * n^(n^2 - 11/24) / (2^(n^2 + 3*n/2 + 17/24) * exp(3*n^2/2 + 1/24)), where A is the Glaisher-Kinkelin constant A074962.

%F a(n) = 3*n*a(n-1)*Product_{i=1..n-1} (2*i+n)(2*n+i). - _Chai Wah Wu_, Feb 26 2019

%F a(n) = a(n-1) * (3*n)! * (3*n-2)!!/((2*n)! * n!!). - _Robert Israel_, Feb 27 2019

%p f:= n -> mul((2*i+n)!/(2*i)!,i=1..n):

%p map(f, [$0..10]); # _Robert Israel_, Feb 27 2019

%t Table[Product[2*i+j, {i, 1, n}, {j, 1, n}], {n, 1, 10}]

%Y Cf. A059486, A079478, A324403, A367956, A367957, A367958.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 26 2019

%E a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2023