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 A014297 #57 Mar 19 2025 14:27:54
%S A014297 2,12,96,960,11520,161280,2580480,46448640,928972800,20437401600,
%T A014297 490497638400,12752938598400,357082280755200,10712468422656000,
%U A014297 342798989524992000,11655165643849728000,419585963178590208000,15944266600786427904000,637770664031457116160000
%N A014297 a(n) = n! * C(n+2, 2) * 2^(n+1).
%C A014297 Partition the set {1,2,...,n+2} into an even number of subsets. Arrange (linearly order) the elements within each subset and then arrange the subsets. - _Geoffrey Critzer_, Mar 03 2010
%H A014297 Vincenzo Librandi, <a href="/A014297/b014297.txt">Table of n, a(n) for n = 0..200</a>
%H A014297 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=506">Encyclopedia of Combinatorial Structures 506</a>
%H A014297 Alexsandar Petojevic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL5/Petojevic/petojevic5.html">The Function vM_m(s; a; z) and Some Well-Known Sequences</a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7.
%F A014297 a(n) = Sum_{k=0..n} (n+2)!*C(n,k).
%F A014297 Prepend the sequence with 1,0, then e.g.f. is (1-x)^2/(1-2*x). - _Geoffrey Critzer_, Mar 03 2010
%F A014297 E.g.f.: 2/(1-2*x)^3. - _R. J. Mathar_, Nov 27 2011
%F A014297 a(n) = 2*A051578(n). - _R. J. Mathar_, Apr 26 2017
%F A014297 a(n) = (n+2)! * 2^n. - _Joerg Arndt_, May 05 2019
%F A014297 From _Amiram Eldar_, Jul 04 2020: (Start)
%F A014297 Sum_{n>=0} 1/a(n) = 4*sqrt(e) - 6.
%F A014297 Sum_{n>=0} (-1)^n/a(n) = 4/sqrt(e) - 2. (End)
%p A014297 seq(count(Permutation(n+1))*count(Composition(n)),n=1..17); # _Zerinvary Lajos_, Oct 16 2006
%t A014297 Drop[CoefficientList[Series[(1-x)^2/(1-2x), {x, 0, 20}], x]* Table[n!, {n, 0, 20}], 2] (* _Geoffrey Critzer_, Mar 03 2010 *)
%t A014297 Part[#, Range[1, Length[#], 1]]&@(Array[#!&, Length[#], 0]*#)&@CoefficientList[Series[2/(1 - 2*x)^3, {x, 0, 20}], x]// ExpandAll (* _Vincenzo Librandi_, Jan 04 2013 - after _Olivier Gérard_ in A213068 *)
%t A014297 Table[n!Binomial[n+2,2]2^(n+1),{n,0,30}] (* _Harvey P. Dale_, Dec 27 2022 *)
%o A014297 (PARI) a(n) = (n+2)!*2^n; \\ _Joerg Arndt_, May 05 2019
%o A014297 (Magma) [2^n*Factorial(n+2): n in [0..20]]; // _G. C. Greubel_, May 05 2019
%o A014297 (Sage) [2^n*factorial(n+2) for n in (0..20)] # _G. C. Greubel_, May 05 2019
%o A014297 (GAP) List([0..20], n-> 2^n*Factorial(n+2)); # _G. C. Greubel_, May 05 2019
%Y A014297 Essentially the same as A052564.
%Y A014297 Cf. A088312.
%K A014297 nonn,easy
%O A014297 0,1
%A A014297 _Emeric Deutsch_