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A014297 n! * C(n+2, 2) * 2^(n+1). 2
2, 12, 96, 960, 11520, 161280, 2580480, 46448640, 928972800, 20437401600, 490497638400, 12752938598400, 357082280755200, 10712468422656000, 342798989524992000, 11655165643849728000, 419585963178590208000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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]

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 506

Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7

FORMULA

Sum((n+2)!*C(n,k), k=0..n).

Prepend the sequence with 1,0, then e.g.f. is (1-x)^2/(1-2x). [Geoffrey Critzer, Mar 03 2010]

E.g.f. 2/(1-2x)^3. - R. J. Mathar, Nov 27 2011

MAPLE

seq(count(Permutation(n+1))*count(Composition(n)), n=1..17); - Zerinvary Lajos, Oct 16 2006

MATHEMATICA

CoefficientList[Series[(1 - x)^2/(1 - 2 x), {x, 0, 20}], x]* Table[n!, {n, 0, 20}] (* Geoffrey Critzer, Mar 03 2010 *)

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 *)

CROSSREFS

Essentially the same as A052564.

Cf. A088312.

Sequence in context: A213422 A153231 * A052564 A193425 A206855 A219119

Adjacent sequences:  A014294 A014295 A014296 * A014298 A014299 A014300

KEYWORD

nonn

AUTHOR

Emeric Deutsch

STATUS

approved

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Last modified December 8 04:27 EST 2016. Contains 278902 sequences.