A134356 a(n) = Product_{k=1..n-1} (3k+1)!/(n+k)!.

1, 4, 42, 1008, 51480, 5353920, 1100473920, 437480709120, 330886851724800, 470053968773760000, 1241242628123282400000, 6040838558884497984000000, 53797620867616662708672000000, 871394214986903051252166758400000

Offset: 1

Author

Artur Jasinski, Oct 22 2007

Keywords

• nonn

Crossrefs

Cf. A005130.

Programs

Mathematica

a = {}; Do[k = Product[(3i + 1)!/(n + i)!, {i, 1, n - 1}]; AppendTo[a, k], {n, 1, 20}]; a
Table[Product[(3k+1)!/(n+k)!,{k,n-1}],{n,20}] (* Harvey P. Dale, Sep 30 2015 *)

Formula

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