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 A293471 #6 Sep 16 2021 14:24:44
%S A293471 1,2,20,248,3472,53152,878144,15577984,296411392,6054973952,
%T A293471 132994708480,3144712222720,80063883022336,2192452931723264,
%U A293471 64427309553434624,2025284853319303168,67859418068644069376,2414526405567056052224,90909088845844899430400,3610058425696043667030016
%N A293471 a(n) = [x^n] (1/(1 - 2*x/(1 - 2*x/(1 - 4*x/(1 - 4*x/(1 - 6*x/(1 - 6*x/(1 - ...))))))))^n, a continued fraction.
%H A293471 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A293471 a(n) ~ sqrt(Pi) * 2^(n + 1/2) * n^(n + 3/2) / exp(n-1). - _Vaclav Kotesovec_, Sep 16 2021
%t A293471 Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-2 Floor[(k + 1)/2] x, 1, {k, 1, n}])^n, {x, 0, n}], {n, 0, 19}]
%t A293471 Table[SeriesCoefficient[Sum[(2 k)!! x^k, {k, 0, n}]^n, {x, 0, n}], {n, 0, 19}]
%Y A293471 Cf. A000165, A052712, A126674, A287899, A293470.
%K A293471 nonn
%O A293471 0,2
%A A293471 _Ilya Gutkovskiy_, Oct 09 2017