|
|
A014297
|
|
a(n) = 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, 15944266600786427904000, 637770664031457116160000
(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
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} (n+2)!*C(n,k).
Prepend the sequence with 1,0, then e.g.f. is (1-x)^2/(1-2*x). - Geoffrey Critzer, Mar 03 2010
Sum_{n>=0} 1/a(n) = 4*sqrt(e) - 6.
Sum_{n>=0} (-1)^n/a(n) = 4/sqrt(e) - 2. (End)
|
|
MAPLE
|
seq(count(Permutation(n+1))*count(Composition(n)), n=1..17); # Zerinvary Lajos, Oct 16 2006
|
|
MATHEMATICA
|
Drop[CoefficientList[Series[(1-x)^2/(1-2x), {x, 0, 20}], x]* Table[n!, {n, 0, 20}], 2] (* 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 *)
Table[n!Binomial[n+2, 2]2^(n+1), {n, 0, 30}] (* Harvey P. Dale, Dec 27 2022 *)
|
|
PROG
|
(Magma) [2^n*Factorial(n+2): n in [0..20]]; // G. C. Greubel, May 05 2019
(Sage) [2^n*factorial(n+2) for n in (0..20)] # G. C. Greubel, May 05 2019
(GAP) List([0..20], n-> 2^n*Factorial(n+2)) # G. C. Greubel, May 05 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|