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%I #22 Sep 08 2022 08:44:51
%S 0,2,8,504,1153152,168275764800,2407165968578342400,
%T 4788742737385049982623884800,
%U 1780642079411485280163076498360356864000,159943989198524502594920793284078996733117111490560000,4353607386405822605116660595502838129080647848043621660449907712000000
%N a(n) = 2*(n^2)!* Product_{k = 1..n-1} k!/(n+k)!.
%H G. C. Greubel, <a href="/A033542/b033542.txt">Table of n, a(n) for n = 0..29</a>
%F a(n) ~ Pi * exp(n^2/2 - n + 1/12) * n^(n^2 + n + 17/12) / (A * 2^(2*n^2 - 25/12)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Oct 15 2019
%p seq(`if`(n=0, 0, 2*factorial(n^2)*mul(factorial(k)/factorial(n+k), k = 1 .. n-1)), n = 0..10); # _G. C. Greubel_, Oct 12 2019
%t Table[If[n==0, 0, 2*(n^2)!*Product[k!/(n+k)!, {k,1,n-1}]], {n,0,10}] (* _G. C. Greubel_, Oct 12 2019 *)
%t Flatten[{0, Table[2*BarnesG[n+1]*BarnesG[n+2]*(n^2)!/BarnesG[2*n + 1], {n, 1, 10}]}] (* _Vaclav Kotesovec_, Oct 15 2019 *)
%o (PARI) concat([0], vector(10, n, 2*(n^2)!*prod(k=1,n-1, k!/(n+k)!) )) \\ _G. C. Greubel_, Oct 12 2019
%o (Magma) [0,2] cat [2*Factorial(n^2)*(&*[Factorial(k)/Factorial(n+k): k in [1..n-1]]): n in [2..10]]; // _G. C. Greubel_, Oct 12 2019
%o (Sage) [0]+[2*factorial(n^2)*product(factorial(k)/factorial(n+k) for k in (1..n-1)) for n in (1..10)] # _G. C. Greubel_, Oct 12 2019
%o (GAP) Concatenation([0], List([1..10], n-> 2*Factorial(n^2)*Product([1..n-1], k-> Factorial(k)/Factorial(n+k)) )); # _G. C. Greubel_, Oct 12 2019
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Feb 13 2002
%E Definition corrected by Neven Juric, Nov 08 2012
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