login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181768 G.f.: (1/2)*(3 - sqrt((1-5*x)/(1-x))). 2
1, 1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965, 803539474345, 3741930523740, 17481709707825, 81912506777200, 384847173838501, 1812610804416698, 8556895079642921, 40480850291739165, 191884148712996795, 911225151259732188, 4334673398737025619, 20653004146207902678, 98551406393189773875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Same as A007317 if the first 1 is omitted. Has several combinatorial interpretations so deserves its own entry.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Ira M. Gessel, Jang Soo Kim, A note on 2-distant noncrossing partitions and weighted Motzkin paths, arXiv:1003.5301 [math.CO], 2010.

Ira M. Gessel, Jang Soo Kim, A note on 2-distant noncrossing partitions and weighted Motzkin paths, Discrete Math. 310 (2010), no. 23, 3421-3425.

FORMULA

a(n) ~ 5^(n+1/2)/(8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 29 2013

Conjecture: n*a(n) +2*(-3*n+4)*a(n-1) +5*(n-2)*a(n-2)=0. - R. J. Mathar, Aug 06 2013

a(n) = JacobiP(n-1,1,-n-1/2,9)/n for n>0. - Peter Luschny, Sep 23 2014

MAPLE

A181768 := n -> `if`(n=0, 1, JacobiP(n-1, 1, -n-1/2, 9)/n):

seq(round(evalf(A181768(n), 99)), n=0..33); # Peter Luschny, Sep 23 2014

MATHEMATICA

CoefficientList[Series[3/2-Sqrt[(1-5x)/(1-x)]/2, {x, 0, 40}], x] (* Harvey P. Dale, Jul 28 2013 *)

PROG

(PARI) x='x + O('x^50); Vec((1/2)*(3 - sqrt((1-5*x)/(1-x)))) \\ G. C. Greubel, Feb 12 2017

CROSSREFS

Cf. A007317.

Sequence in context: A124303 A073525 A007317 * A279554 A279555 A153197

Adjacent sequences:  A181765 A181766 A181767 * A181769 A181770 A181771

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 12 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 29 15:31 EDT 2017. Contains 284273 sequences.