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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000777 a(n) = (n+2)*Catalan(n)-1. 3
1, 2, 7, 24, 83, 293, 1055, 3860, 14299, 53481, 201551, 764217, 2912167, 11143499, 42791039, 164812364, 636438059, 2463251009, 9552773999, 37112526989, 144410649239, 562724141459, 2195581527359, 8576490341249, 33537507830423, 131272552839203, 514285886020255 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

T. D. Noe, Table of n, a(n) for n = 0..200

C. K. Fan, Structure of a Hecke algebra quotient, J. Amer. Math. Soc. 10 (1997), no. 1, 139-167.

J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.

FORMULA

a(n) = (binomial(2*n,n)/(n+1))*(n+2)-1 - Zerinvary Lajos, Jun 25 2006

G.f.: 1/2+(6x-1)/(2sqrt(1-4x)-x/(1-x). [Vladimir Kruchinin, Aug 18 2010]

MAPLE

[seq((binomial(2*n, n)/(n+1))*(n+2)-1, n=0..27)]; # Zerinvary Lajos, Jun 25 2006

MATHEMATICA

Table[(n + 2)*CatalanNumber[n] - 1, {n, 0, 20}] (* T. D. Noe, Jun 20 2012 *)

PROG

(PARI) a(n) = (n+2)*binomial(2*n, n)/(n+1) - 1; \\ Michel Marcus, Sep 11 2016

(MAGMA) [(n+2)*Catalan(n)-1: n in [0..30]]; // Vincenzo Librandi, Sep 11 2016

CROSSREFS

a(n) = A038665(n-1) - 1.

Cf. A000984, A000108.

Sequence in context: A003480 A020727 A088854 * A144170 A297345 A052986

Adjacent sequences:  A000774 A000775 A000776 * A000778 A000779 A000780

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 16:08 EDT 2019. Contains 322461 sequences. (Running on oeis4.)