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A082292 a(n) = (2n+1) * (2n)! / sqrt(4*(n+1)*Product_{k=1..2n+1} lcm(k, 2n+2-k)).

%I A082292 #10 Jan 07 2021 21:14:01
%S A082292 1,1,2,12,4,8,72,160,16,3456,32,1792,129600,1024,128,1492992,256,
%T A082292 2048000,18289152,180224,1024,573308928,1280000,1703936,241864704,
%U A082292 719323136,8192,64497254400000,16384,33554432,234125033472,142606336
%N A082292 a(n) = (2n+1) * (2n)! / sqrt(4*(n+1)*Product_{k=1..2n+1} lcm(k, 2n+2-k)).
%t A082292 Table[((2n+1)(2n)!)/Sqrt[4(n+1)Product[LCM[k,2n+2-k],{k,2n+1}]],{n,2,40}] (* _Harvey P. Dale_, Aug 01 2020 *)
%o A082292 (PARI) for(i=2, 20, n=i*2+1; p=1; for(k=1, n, p=p*lcm(k, n+1-k)); print1((2*i+1)*(2*i)!/sqrtint(4*(i+1)*p)", "))
%Y A082292 Cf. A082022.
%K A082292 nonn
%O A082292 2,3
%A A082292 _Ralf Stephan_, Apr 08 2003