This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A277347 #27 Sep 10 2023 18:09:04
%S A277347 1,5,65,1625,66625,4064125,345450625,39035920625,5660208490625,
%T A277347 1024497736803125,226413999833490625,59999709955875015625,
%U A277347 18779909216188879890625,6854666863908941160078125,2885814749705664228392890625,1388076894608424493856980390625,756501907561591349152054312890625
%N A277347 a(n) = Product_{k=1..n} (2*k*(k-1)+1).
%C A277347 Fang (see link) proves that a(n) is never a square for n > 1.
%H A277347 Jin-Hui Fang, <a href="https://www.emis.de/journals/INTEGERS/papers/j16/j16.Abstract.html">Neither Product{k=1..n} (4k^2+1) nor Product{k=1..n} (2k(k-1)+1) is a perfect square</a>, Integers, A16, Volume 9 (2009).
%F A277347 a(n) ~ cosh(Pi/2) * 2^(n+1) * n^(2*n) / exp(2*n). - _Vaclav Kotesovec_, Oct 10 2016
%F A277347 a(n) = 2^n * |Gamma(1/2 + i/2 + n)|^2 * cosh(Pi/2)/Pi. - _Vladimir Reshetnikov_, Oct 11 2016
%F A277347 E.g.f.: 2F0((1-i)/2,(1+i)/2; ; 2*x). - _Benedict W. J. Irwin_, Oct 19 2016
%F A277347 a(n) = 2^(-1 + n)*Pochhammer(3/2 - i/2, -1 + n)*Pochhammer(3/2 + i/2, -1 + n), for n>=1. - _Antonio Graciá Llorente_, Sep 10 2023
%t A277347 Table[Product[(2*k*(k-1)+1), {k,1,n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Oct 10 2016 *)
%t A277347 Round@Table[2^n Abs[Gamma[1/2 + I/2 + n]]^2 Cosh[Pi/2]/Pi, {n, 1, 20}] (* _Vladimir Reshetnikov_, Oct 11 2016 *)
%t A277347 Rest@(CoefficientList[Series[HypergeometricPFQ[{1/2 - I/2, 1/2 + I/2}, {}, 2 x], {x, 0, 20}], x]*Range[0, 20]!) (* _Benedict W. J. Irwin_, Oct 19 2016 *)
%o A277347 (PARI) a(n) = prod(k=1, n, 2*k*(k-1)+1);
%Y A277347 Cf. A001844.
%K A277347 nonn
%O A277347 1,2
%A A277347 _Michel Marcus_, Oct 10 2016