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 A052564 #29 Jul 18 2025 13:20:27
%S A052564 0,1,2,12,96,960,11520,161280,2580480,46448640,928972800,20437401600,
%T A052564 490497638400,12752938598400,357082280755200,10712468422656000,
%U A052564 342798989524992000,11655165643849728000,419585963178590208000
%N A052564 Expansion of e.g.f. x*(1-x)/(1-2*x).
%C A052564 Partition the set {1,2,...,n} into an odd number of subsets, arrange (linearly order) the elements within each subset, then arrange the subsets. - _Geoffrey Critzer_, Mar 05 2010
%H A052564 Vincenzo Librandi, <a href="/A052564/b052564.txt">Table of n, a(n) for n = 0..200</a>
%H A052564 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=506">Encyclopedia of Combinatorial Structures 506</a>
%F A052564 E.g.f.: x*(1-x)/(1-2*x).
%F A052564 a(n) = 2*n*a(n-1), with a(0)=0, a(1)=1, a(2)=2.
%F A052564 a(n) = 2^(n-2) * n! for n>1.
%F A052564 a(n) = A002866(n) - A014297(n-2) for n>1. - _Geoffrey Critzer_, Mar 05 2010
%p A052564 spec := [S,{S=Prod(Z,Sequence(Prod(Z,Sequence(Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052564 a = x/(1 - x); CoefficientList[Series[a/(1 - a^2), {x, 0, 20}], x]* Table[n!, {n, 0, 20}] (* _Geoffrey Critzer_, Mar 05 2010 *)
%t A052564 Part[#,Range[1, Length[#], 1]]&@(Array[#!&, Length[#], 0]*#)&@CoefficientList[Series[x*(1-x)/(1-2x), {x, 0, 20}], x]// ExpandAll (* _Vincenzo Librandi_, Jan 04 2013 - after _Olivier Gérard_ in A213068 *)
%t A052564 With[{nn=20},CoefficientList[Series[x (1-x)/(1-2x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 18 2025 *)
%o A052564 (PARI) {a(n) = if(n<=1, n, 2^(n-2)*n!)}; \\ _G. C. Greubel_, May 05 2019
%o A052564 (Magma) [n le 1 select n else 2^(n-2)*Factorial(n): n in [0..20]]; // _G. C. Greubel_, May 05 2019
%o A052564 (Sage) [0,1]+[2^(n-2)*factorial(n) for n in (2..20)] # _G. C. Greubel_, May 05 2019
%o A052564 (PARI) my(x='x+O('x^20)); concat([0], Vec(serlaplace(x*(1-x)/(1-2*x)))) \\ _Felix Fröhlich_, May 05 2019
%Y A052564 Essentially the same as A014297.
%K A052564 easy,nonn
%O A052564 0,3
%A A052564 encyclopedia(AT)pommard.inria.fr, Jan 25 2000