%I #15 May 11 2018 10:17:44
%S 1,2,112,261360,27983155200,143829595278720000,
%T 36441048083860298170220544,463109968103790656729135319264000000,
%U 298869615482782118878970689211942578421760000000
%N a(n) = sqrt( binomial(4n,0) * binomial(4n,1) * ... * binomial(4n,2n-1) ).
%H G. C. Greubel, <a href="/A165975/b165975.txt">Table of n, a(n) for n = 0..25</a>
%F a(n) = (4n)!^n / A165970(n).
%F a(n) ~ A^(1/2) * exp(2*n^2 + n - 1/48) / (2^(5*n/2 + 1/6) * Pi^(n/2) * n^(n/2 - 1/24)), where A = A074962 is the Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, Apr 19 2016
%t Table[Sqrt[Product[Binomial[4*n, k], {k, 0, 2*n - 1}]], {n, 0, 5}] (* _G. C. Greubel_, Apr 19 2016 *)
%o (PARI) a(n) = sqrtint(prod(k=0, 2*n-1, binomial(4*n, k))); \\ _Michel Marcus_, Apr 19 2016
%Y Cf. A262261.
%K nonn
%O 0,2
%A _Max Alekseyev_, Oct 02 2009