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A272166 a(n) = Product_{k=0..n} (k*n-k)!. 2

%I

%S 1,1,2,34560,750902834626560000,

%T 23594617426193665303453830729600860160000000000

%N a(n) = Product_{k=0..n} (k*n-k)!.

%C The next term has 97 digits.

%F a(n) ~ A^(n-1) * n^(1/6 + n/12 + n^3) * (2*Pi)^(n/2 + 1/4) / exp((2 + 3*n + 3*n^2 + 9*n^3)/12), where A = A074962 is the Glaisher-Kinkelin constant.

%t Table[Product[(k*n-k)!, {k, 0, n}], {n, 0, 8}]

%Y Cf. A272165.

%K nonn,easy

%O 0,3

%A _Vaclav Kotesovec_, Apr 21 2016

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Last modified October 22 01:46 EDT 2020. Contains 337948 sequences. (Running on oeis4.)