%I #31 Sep 08 2022 08:45:32
%S 1,3,135,212625,21097715625,207248662456171875,
%T 291128066470548703880859375,79746389028864195813528714933837890625,
%U 5570294521107277357810167397301815834831695556640625
%N a(n) = Product_{k=1..n} (2*k-1)^(2*n-2*k+1).
%H G. C. Greubel, <a href="/A136411/b136411.txt">Table of n, a(n) for n = 1..29</a>
%F a(n) = A107254(n) / 2^(n*(n - 1)).
%F a(n) = sf(2*n-1) / (2^(n*(n-1)) * sf(n-1)^2), n >= 1, where sf(n) = BarnesG(n + 2) is the superfactorial defined in A000178. - _Robert Coquereaux_, Apr 02 2013
%F a(n) ~ A * 2^(n^2 + n - 1/12) * n^(n^2 + 1/12) / exp(3*n^2/2 + 1/12), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, Jul 10 2015
%t Table[Product[(2*k - 1)^(2*n - 2*k + 1), {k, 1, n}], {n, 1, 10}] (* _Stefan Steinerberger_, May 18 2008 *)
%t sf[n_] := BarnesG[n + 2]; a[n_] := sf[2 n - 1]/(2^(n (n - 1)) sf[n - 1]^2); Table[a[n], {n, 1, 10}] (* _Robert Coquereaux_, Apr 02 2013 *)
%o (PARI) a(n) = prod(k=1, n, (2*k-1)^(2*n-2*k+1)) \\ _Anders Hellström_, Sep 16 2015
%o (Magma) [(&*[(2*k-1)^(2*n-2*k+1): k in [1..n]]): n in [1..10]]; // _G. C. Greubel_, Oct 14 2018
%Y Cf. A136807, A087315, A000178, A055209.
%K easy,nonn
%O 1,2
%A _Ctibor O. Zizka_, Mar 31 2008
%E More terms from _Stefan Steinerberger_, May 18 2008