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 A032184 #71 Feb 02 2023 02:30:11
%S A032184 1,4,16,96,768,7680,92160,1290240,20643840,371589120,7431782400,
%T A032184 163499212800,3923981107200,102023508787200,2856658246041600,
%U A032184 85699747381248000,2742391916199936000,93241325150797824000,3356687705428721664000,127554132806291423232000
%N A032184 a(n) = 2^n*(n-1)! for n > 1, a(1) = 1.
%C A032184 Previous name was: "CIJ" (necklace, indistinct, labeled) transform of 1, 3, 5, 7, ...
%H A032184 C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>.
%H A032184 Guo-Niu Han, <a href="/A196265/a196265.pdf">Enumeration of Standard Puzzles</a>, 2011. [Cached copy]
%H A032184 Guo-Niu Han, <a href="https://arxiv.org/abs/2006.14070">Enumeration of Standard Puzzles</a>, arXiv:2006.14070 [math.CO], 2020.
%H A032184 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=565">Encyclopedia of Combinatorial Structures 565</a>.
%H A032184 <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>.
%F A032184 a(n) = 2^n*(n-1)! for n > 1, a(1) = 1.
%F A032184 E.g.f.: (1 + 2*x)/(1 - 2*x). - _Paul Barry_, May 26 2003 [This e.g.f. yields the sequence (a(n+1): n >= 0). - _M. F. Hasler_, Jan 15 2017]
%F A032184 a(n) + 2*(-n+1)*a(n-1) = 0. - _R. J. Mathar_, Nov 30 2012 [Valid for n >= 3; equivalently: a(n+1) = 2*n*a(n) for n > 1. - _M. F. Hasler_, Jan 15 2017]
%F A032184 G.f.: G(0) - 1, where G(k) = 1 + 1/(1 - 1/(1 + 1/((2*k + 2)*x*G(k+1)))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 14 2013
%F A032184 Let s(n) = Sum_{k >= 1} 1/(2*k - 1)^n with n > 1, then s(n) = (-1)^n*PolyGamma(n-1, 1/2)/a(n). - _Jean-François Alcover_, Dec 18 2013
%F A032184 a(n) = round(-zeta(n)(1/2)) where zeta(n)(1/2) is the n-th derivative of the zeta function at 1/2. - _Artur Jasinski_, Feb 06 2021
%F A032184 E.g.f.: -x-log(1-2*x). - _Alois P. Heinz_, Mar 10 2022
%F A032184 Sum_{n>=1} 1/a(n) = (exp(1/2)+1)/2. - _Amiram Eldar_, Feb 02 2023
%p A032184 A032184:=n->if n>1 then 2^n*(n-1)! else 1 fi: seq(A032184(n), n=1..30); # _Wesley Ivan Hurt_ and _M. F. Hasler_, Jan 15 2017
%t A032184 Join[{1},Table[2^n (n-1)!,{n,2,20}]] (* _Harvey P. Dale_, Oct 08 2017 *)
%o A032184 (PARI) apply( A032184=n->(n-1)!<<n-(n==1) , [1..18]) \\ _M. F. Hasler_, Jan 15 2017
%Y A032184 Apart from the initial term, same as A066318.
%K A032184 nonn,easy
%O A032184 1,2
%A A032184 _Christian G. Bower_
%E A032184 New name (using first formula) from _Joerg Arndt_, Mar 10 2022