|
| |
|
|
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 (zerinvarylajos(AT)yahoo.com), 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
|
| |
|
|
