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a(n) = Product_{k=0..n} (n^2-k)^k.
4

%I #10 Apr 23 2016 08:12:40

%S 0,12,84672,133937556480,84132174409113600000,

%T 31820251569524195280814080000000,

%U 10171374668270380199596141241071328726876160000,3665849746122305381874580384965936229566478146157181833052160000

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

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

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

%t Table[Product[(n^2-k)^k, {k, 0, n}], {n, 1, 10}]

%t 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}]

%Y Cf. A272164, A272237.

%K nonn,easy

%O 1,2

%A _Vaclav Kotesovec_, Apr 21 2016