A272167 a(n) = Product_{k=2..n} (k^2-k)^k.

1, 4, 864, 17915904, 57330892800000, 41794220851200000000000, 9635211808655307020697600000000000, 931891782579353562478377930946353561600000000000, 48457159197906991133853954271145046614004301737177907200000000000

Offset: 1

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

• nonn
• easy

Crossrefs

Cf. A002109, A272168.

Programs

Mathematica

Table[Product[(k^2-k)^k, {k, 2, n}], {n, 1, 10}]
Table[n^n * Gamma[n]^(2*n-1) / BarnesG[n]^2, {n,1,10}] (* Vaclav Kotesovec, Apr 21 2024 *)

PARI

a(n) = prod(k=2, n, (k^2-k)^k); \\ Michel Marcus, Nov 18 2021

Formula

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

a(n) = n^n * Gamma(n)^(2*n-1) / BarnesG(n)^2. - Vaclav Kotesovec, Apr 21 2024

Extensions

Definition corrected by Georg Fischer, Nov 18 2021