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%I #6 Oct 26 2017 16:47:29
%S 1,4,42,1008,51480,5353920,1100473920,437480709120,330886851724800,
%T 470053968773760000,1241242628123282400000,6040838558884497984000000,
%U 53797620867616662708672000000,871394214986903051252166758400000
%N a(n) = Product_{k=1..n-1} (3k+1)!/(n+k)!.
%F a(n) ~ Pi^(5/6) * 3^(3*n^2/2 - 7/36) * n^(n + 13/36) / (A^(1/3) * Gamma(1/3)^(2/3) * 2^(2*n^2 - 11/12) * exp(n - 1/36)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Oct 26 2017
%t a = {}; Do[k = Product[(3i + 1)!/(n + i)!, {i, 1, n - 1}]; AppendTo[a, k], {n, 1, 20}]; a
%t Table[Product[(3k+1)!/(n+k)!,{k,n-1}],{n,20}] (* _Harvey P. Dale_, Sep 30 2015 *)
%Y Cf. A005130.
%K nonn
%O 1,2
%A _Artur Jasinski_, Oct 22 2007
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