|
| |
|
|
A005317
|
|
(2^n + C(2*n,n))/2.
(Formerly M1460)
|
|
3
| |
|
|
1, 2, 5, 14, 43, 142, 494, 1780, 6563, 24566, 92890, 353740, 1354126, 5204396, 20066492, 77575144, 300572963, 1166868646, 4537698722, 17672894044, 68923788698, 269129985796, 1052051579012, 4116719558104, 16123810230158, 63205319996092, 247959300028484
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Hankel transform is A008619. - Paul Barry (pbarry(AT)wit.ie), Nov 13 2007
|
|
|
REFERENCES
| T. Klove, Generating functions for the number of permutations with limited displacement, Electron. J. Combin., 16 (2009), #R104. - From N. J. A. Sloane, May 04 2011.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..178
Plouffe, Simon, Master Thesis, copy at the arXiv site
|
|
|
FORMULA
| Contribution from Simon Plouffe, Feb 18 2011: (Start)
G.f.: (1/2)*(-4*x+1+(-(4*x-1)*(2*x-1)^2)^(1/2))/(4*x-1)/(2*x-1).
Recurrence : 0=(-24-28*n-8*n^2)*a(n+1)+(18+22*n+6*n^2)*a(n+2)+
(-3-4*n-n^2)*a(n+3), a(0)=1, a(1)=2, a(2)=5. (End)
a(n) = sum(k=0..floor(n/2),(-1)^k*C(2*n,n-2*k)) , n>0. [From Mircea Merca (mircea.merca(AT)profinfo.edu.ro), Jun 20 2011]
E.g.f.: (exp(2*x)*(1+BesselI(0,2*x))/2 = G(0)/2 ; G(k) = 1+(k)!/(P-2*x*(2*k+1)*(P^2)/(2*x*(2*k+1)*P+(k+1)^2*k!/G(k+1))), where P:=((2*k)!)/(2^k)/((k)!) ; -(continued fraction). - Sergei N. Gladkovskii, Dec 20 2011
|
|
|
MAPLE
| f := n->(2^n+binomial(2*n, n))/2;
|
|
|
PROG
| (MAGMA) [(2^n+Binomial(2*n, n))/2: n in [0..26]]; // Bruno Berselli, Jun 20 2011
(Maxima) makelist(sum((-1)^k*binomial(2*n, n-2*k), k, 0, floor(n/2)), n, 0, 26); [Bruno Berselli, Jun 20 2011]
(PARI) a(n)=(2^n+binomial(2*n, n))/2 \\ Charles R Greathouse IV, Dec 20 2011
|
|
|
CROSSREFS
| Sequence in context: A181496 A029889 A123020 * A126566 A112808 A088927
Adjacent sequences: A005314 A005315 A005316 * A005318 A005319 A005320
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and Peter Fishburn.
|
| |
|
|
