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A156266 a(n) = 7^n*Catalan(n). 7
1, 7, 98, 1715, 33614, 705894, 15529668, 353299947, 8243665430, 196199237234, 4744454282204, 116239129913998, 2879153833254412, 71978845831360300, 1813866914950279560, 46026872966863343835, 1175038992212864189670 (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) = 7^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:

7, 7, 0, 0, 0, 0,...

7, 7, 7, 0, 0, 0,...

7, 7, 7, 7, 0, 0,...

7, 7, 7, 7, 7, 0,...

... (End)

E.g.f.: KummerM(1/2, 2, 28*x). - Peter Luschny, Aug 26 2012

G.f.: c(7*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)*6^k. - Philippe Deléham, Nov 15 2013

G.f.: 1/(1 - 7*x/(1 - 7*x/(1 - 7*x/(1 - ...)))), a continued fraction. - Ilya Gutkovskiy, Aug 08 2017

MAPLE

A156266_list := proc(n) local j, a, w; a := array(0..n); a[0] := 1;

for w from 1 to n do a[w] := 7*(a[w-1]+add(a[j]*a[w-j-1], j=1..w-1)) od; convert(a, list)end: A156266_list(16); # Peter Luschny, May 19 2011

PROG

(MAGMA) [7^n*Catalan(n): n in [0..20]]; // Vincenzo Librandi, Jul 19 2011

CROSSREFS

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

Column k=7 of A290605.

Sequence in context: A219406 A267664 A237022 * A234873 A051188 A113134

Adjacent sequences:  A156263 A156264 A156265 * A156267 A156268 A156269

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 June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)