A272163 a(n) = Product_{k=0..n} (n^2-k)^k.

0, 12, 84672, 133937556480, 84132174409113600000, 31820251569524195280814080000000, 10171374668270380199596141241071328726876160000, 3665849746122305381874580384965936229566478146157181833052160000

Offset: 1

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

• nonn
• easy

Crossrefs

Cf. A272164, A272237.

Programs

Mathematica

Table[Product[(n^2-k)^k, {k, 0, n}], {n, 1, 10}]
Table[BarnesG[n^2 + 2] * (n-1)^n * n^n * Pochhammer[1 - n + n^2, n]^n / (((n^2)!)^(n+1) * BarnesG[n^2 - n + 1]), {n, 1, 10}]

Formula

a(n) = A272164(n) * A272179(n)^n / ((n^2)!)^(n+1).

a(n) ~ n^(n*(n+1)) / exp(n/3 + 5/8).