A294319 - OEIS

%I #7 Sep 26 2023 15:19:57

%S 2,240,9676800,386266890240000,33674087438261157888000000,

%T 11977449554394932435557703221248000000000,

%U 29139961073721833036780987632259240162985246720000000000000

%N a(n) = Product_{k=0..n} (3*k + 2)!.

%F a(n) ~ 3^(3*n^2/2 + 4*n + 101/36) * (2*Pi)^(n/2 + 1/3) * n^(3*n^2/2 + 4*n + 91/36) * Gamma(1/3)^(1/3) / (A^(1/3) * exp(9*n^2/4 + 4*n - 1/36)), where A is the Glaisher-Kinkelin constant A074962.

%F A268504(n) * A294318(n) * A294319(n) = A000178(3*n + 2).

%t Table[Product[(3*k + 2)!, {k, 0, n}] , {n, 0, 10}]

%t FoldList[Times,(3 Range[0,10]+2)!] (* _Harvey P. Dale_, Sep 26 2023 *)

%Y Cf. A268504, A294318.

%K nonn

%O 0,1

%A _Vaclav Kotesovec_, Oct 28 2017