|
| |
|
|
A052591
|
|
E.g.f. x/((1-x)(1-x^2)).
|
|
4
| |
|
|
0, 1, 2, 12, 48, 360, 2160, 20160, 161280, 1814400, 18144000, 239500800, 2874009600, 43589145600, 610248038400, 10461394944000, 167382319104000, 3201186852864000, 57621363351552000, 1216451004088320000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Stirling transform of 2*a(n)=[2,4,24,96,...] is A052841(n+1)=[2,6,38,270,...]. - Michael Somos Mar 04 2004
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 18 2009: (Start)
a(n) is the number of even fixed points in all permutations of {1,2,...,n+1}. Example: a(2)=2 because we have 12'3, 132, 312, 213, 231, and 32'1, the even fixed points being marked.
a(n)=(n+1)! - A052558(n).
(End)
|
|
|
LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 536
|
|
|
FORMULA
| Recurrence: {a(1)=1, a(0)=0, (-n^3-5*n^2-8*n-4)*a(n)+(-2-n)*a(n+1)+(n+1)*a(n+2)=0}
(1/4*(-1)^(1-n)+1/2*n+1/4)*n!
E.g.f.: x/((1-x)(1-x^2)).
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 18 2009: (Start)
a(n)=(n+1)!/2 if n is odd; a(n)=n!n/2 if n is even.
(End)
a(n) = n!*A008619(n-1), n>1. - R. J. Mathar, Nov 27 2011
|
|
|
MAPLE
| spec := [S, {S=Prod(Z, Sequence(Z), Sequence(Prod(Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
a:=n->(-1)*sum((-1)^k * (n-k+1) * n!, k=1..n) : seq(a(n), n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 18 2007
a:=n->(n+1)!-sum((-1)^k*n!, k=0..n): seq(a(n)/2, n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2008
restart: G(x):=x/(1-x)/(1-x^2): f[0]:=G(x): for n from 1 to 19 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..19); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, n!*polcoeff(x/(1-x)/(1-x^2)+x*O(x^n), n))
|
|
|
CROSSREFS
| A052558 [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 18 2009]
Sequence in context: A048501 A001815 A052569 * A029766 A088311 A052588
Adjacent sequences: A052588 A052589 A052590 * A052592 A052593 A052594
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
| |
|
|
