A061719 a(n) = Product_{k=0...n} (k!^3).

1, 1, 8, 1728, 23887872, 41278242816000, 15407021574586368000000, 1972469516114225950359552000000000, 129292064547357027522197559428775936000000000000

Offset: 0

Author

Jason Earls, Jun 20 2001

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n=0..27

Crossrefs

Cf. A000178.

Programs

Mathematica

Table[Product[k!^3, {k, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, Nov 23 2023 *)

PARI

for(n=0,11,print(prod(k=1,n,factorial(k)^3)))

PARI

{ for (n=0, 27, write("b061719.txt", n, " ", prod(k=2, n, k!^3)) ) } \\ Harry J. Smith, Jul 26 2009

Formula

a(n) = a(n-1)*A000442(n). - R. J. Mathar, Sep 26 2020

From Vaclav Kotesovec, Nov 23 2023: (Start)

a(n) = A000178(n)^3.

a(n) ~ (2*Pi)^(3*n/2 + 3/2) * n^(3*n^2/2 + 3*n + 5/4) / (A^3 * exp(9*n^2/4 + 3*n - 1/4)), where A is the Glaisher-Kinkelin constant A074962. (End)

Extensions

Terms corrected according to Jason Earls's instructions by Harry J. Smith, Jul 26 2009