login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A156273 a(n) = 9^n*Catalan(n). 5
1, 9, 162, 3645, 91854, 2480058, 70150212, 2051893701, 61556811030, 1883638417518, 58564030799196, 1844766970174674, 58748732742485772, 1888352123865614100, 61182608813245896840, 1996082612532147384405, 65518476340761072970470, 2162109719245115408025510 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = 9^n*A000108(n).

From Gary W. Adamson, Jul 18 2011: (Start)

a(n) = upper left term in M^n, M = an infinite square production matrix as follows:

  9, 9, 0, 0, 0, 0,...

  9, 9, 9, 0, 0, 0,...

  9, 9, 9, 9, 0, 0,...

  9, 9, 9, 9, 9, 0,...

... (end)

E.g.f.: KummerM(1/2, 2, 36*x). - Peter Luschny, Aug 26 2012

G.f.: c(9*x) with c(x) the o.g.f. of A000108 (Catalan). - Philippe Deléham, Nov 15 2013

a(n) = Sum{k=0..n} A085880(n,k)*8^k. - Philippe Deléham, Nov 15 2013

G.f.: 1/(1 - 9*x/(1 - 9*x/(1 - 9*x/(1 - ...)))), a continued fraction. - Ilya Gutkovskiy, Aug 08 2017

MATHEMATICA

Table[9^n CatalanNumber[n], {n, 0, 20}] (* Harvey P. Dale, Sep 09 2012 *)

PROG

(MAGMA)[9^n*Catalan(n): n in [0..20]]; // Vincenzo Librandi, Jul 19 2011

CROSSREFS

Cf. A000108, A151374, A005159, A151403, A156058, A156128, A156266, A156270.

Column k=9 of A290605.

Sequence in context: A157553 A202438 A237024 * A051232 A157574 A077280

Adjacent sequences:  A156270 A156271 A156272 * A156274 A156275 A156276

KEYWORD

nonn

AUTHOR

Philippe Deléham, Feb 07 2009

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 May 13 07:08 EDT 2021. Contains 343836 sequences. (Running on oeis4.)