A324402 a(n) = Product_{i=1..n, j=1..n} (2*i + j).
1, 3, 360, 6350400, 36212520960000, 117563342374788710400000, 337905477880065368190647009280000000, 1234818479230749311108497004714406224855040000000000, 7795494015765035913020359514023640290443493305037073940480000000000000
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..25
Programs
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Maple
f:= n -> mul((2*i+n)!/(2*i)!,i=1..n): map(f, [$0..10]); # Robert Israel, Feb 27 2019
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Mathematica
Table[Product[2*i+j, {i, 1, n}, {j, 1, n}], {n, 1, 10}]
Formula
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.
a(n) = 3*n*a(n-1)*Product_{i=1..n-1} (2*i+n)(2*n+i). - Chai Wah Wu, Feb 26 2019
a(n) = a(n-1) * (3*n)! * (3*n-2)!!/((2*n)! * n!!). - Robert Israel, Feb 27 2019
Extensions
a(0)=1 prepended by Alois P. Heinz, Jun 24 2023