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A156275 a(n) = 10^n*Catalan(n). 3
1, 10, 200, 5000, 140000, 4200000, 132000000, 4290000000, 143000000000, 4862000000000, 167960000000000, 5878600000000000, 208012000000000000, 7429000000000000000, 267444000000000000000, 9694845000000000000000, 353576700000000000000000 (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) = 10^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:

  10, 10, 0, 0, 0,...

  10, 10, 10, 0, 0,...

  10, 10, 10, 10, 0,...

  10, 10, 10, 10, 10,...

... (end)

E.g.f.: KummerM(1/2, 2, 40*x). - Peter Luschny, Aug 26 2012

G.f.: c(10*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)*9^k. - Philippe Deléham, Nov 15 2013

G.f.: 1/(1 - 10*x/(1 - 10*x/(1 - 10*x/(1 - ...)))), a continued fraction. - Ilya Gutkovskiy, Aug 08 2017

MATHEMATICA

Table[10^n CatalanNumber[n], {n, 0, 20}] (* Harvey P. Dale, Mar 12 2013 *)

PROG

(MAGMA) [10^n*Catalan(n): n in [0..20]]; // Vincenzo Librandi, Jul 19 2011

CROSSREFS

Cf. A000108, A151374, A005159, A151403, A156058, A156128, A156266, A156270, A156273.

Column k=10 of A290605.

Sequence in context: A202436 A320671 A237025 * A036362 A051262 A178020

Adjacent sequences:  A156272 A156273 A156274 * A156276 A156277 A156278

KEYWORD

nonn

AUTHOR

Philippe Deléham, Feb 07 2009

EXTENSIONS

a(15) corrected by Vincenzo Librandi, Jul 19 2011

STATUS

approved

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Last modified May 8 08:30 EDT 2021. Contains 343658 sequences. (Running on oeis4.)