A052564 Expansion of e.g.f. x*(1-x)/(1-2*x).

0, 1, 2, 12, 96, 960, 11520, 161280, 2580480, 46448640, 928972800, 20437401600, 490497638400, 12752938598400, 357082280755200, 10712468422656000, 342798989524992000, 11655165643849728000, 419585963178590208000

Offset

0,3

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 506

Formula

E.g.f.: x*(1-x)/(1-2*x).

a(n) = 2*n*a(n-1), with a(0)=0, a(1)=1, a(2)=2.

a(n) = 2^(n-2) * n! for n>1.

a(n) = A002866(n) - A014297(n-2) for n>1. - Geoffrey Critzer, Mar 05 2010

Maple

spec := [S, {S=Prod(Z, Sequence(Prod(Z, Sequence(Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

a = x/(1 - x); CoefficientList[Series[a/(1 - a^2), {x, 0, 20}], x]* Table[n!, {n, 0, 20}] (* Geoffrey Critzer, Mar 05 2010 *)
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 *)

Prog

(PARI) {a(n) = if(n<=1, n, 2^(n-2)*n!)}; \\ G. C. Greubel, May 05 2019
(Magma) [n le 1 select n else 2^(n-2)*Factorial(n): n in [0..20]]; // G. C. Greubel, May 05 2019
(Sage) [0, 1]+[2^(n-2)*factorial(n) for n in (2..20)] # G. C. Greubel, May 05 2019
(PARI) my(x='x+O('x^20)); concat([0], Vec(serlaplace(x*(1-x)/(1-2*x)))) \\ Felix Fröhlich, May 05 2019

Crossrefs

Essentially the same as A014297.

Sequence in context: A307103 A153231 A365282 * A014297 A193425 A206855

Adjacent sequences: A052561 A052562 A052563 * A052565 A052566 A052567

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Status

approved