A125760 a(n) = Product_{k=1..n} A002109(k).

1, 1, 4, 432, 11943936, 1031956070400000, 4159895825138319360000000000, 13809882382682787973867537170432000000000000000, 769161257109634779902443718589603914508004789479014400000000000000000000, 16596916396875768196482032091931000424134701157007816971266990744831779993781534720000000000000000000000000

Offset: 0

Author

N. J. A. Sloane, based on a suggestion from J. M. Bergot, Feb 06 2007

Keywords

• nonn

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..18

Crossrefs

Cf. A002109, A255269.

Programs

Maple

seq(mul(mul(mul(k,j=1..k), k=1..m), m=1..n), n=0..9); # Zerinvary Lajos, Jun 01 2007

Mathematica

Table[Product[Gamma[1 + k]^k/BarnesG[1 + k], {k, 1, n}], {n, 0, 10}] (* Vaclav Kotesovec, Nov 19 2023 *)
Table[BarnesG[n + 2]^n/Product[BarnesG[k]^2, {k, 1, n + 1}], {n, 0, 10}] (* Vaclav Kotesovec, Nov 19 2023 *)

Formula

From Vaclav Kotesovec, Nov 19 2023: (Start)

a(n) = BarnesG(n+2)^n / Product_{k=1..n+1} BarnesG(k)^2.

a(n) ~ A^(n+1) * n^(n^3/6 + n^2/2 + 5*n/12 + 1/12) / exp(5*n^3/36 + n^2/4 + n/12 + zeta(3)/(4*Pi^2)), where A is the Glaisher-Kinkelin constant A074962. (End)