The On-Line Encyclopedia of Integer Sequences (OEIS)

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A120997

Denominators of partial sums of Catalan numbers scaled by powers of 1/9.
(history; published version)

#4 by Russ Cox at Sat Mar 31 13:20:12 EDT 2012

AUTHOR

_Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), _, Aug 16 2006

Discussion

Sat Mar 31

13:20

OEIS Server: https://oeis.org/edit/global/878

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

FORMULA

a(n)=denominator(r(n)) with r(n) := rI(p=1,n) = sum(C(k)/L(2)^(2*k),k=0..n), with Lucas L(2)=3, and C(k):=A000108(k) (Catalan).

KEYWORD

nonn,frac,easy,new

#2 by N. J. A. Sloane at Mon Oct 09 03:00:00 EDT 2006

FORMULA

a(n)=denominator(r(n)) with r(n) := rrI(p=1,n) = sum(C(k)/L(2)^(2*k),k=0..n), with Lucas L(2)=3, and C(k):=A000108(k) (Catalan).

KEYWORD

nonn,frac,easy,new

#1 by N. J. A. Sloane at Fri Sep 29 03:00:00 EDT 2006

NAME

Denominators of partial sums of Catalan numbers scaled by powers of 1/9.

DATA

1, 9, 81, 729, 6561, 19683, 177147, 1594323, 43046721, 387420489, 3486784401, 31381059609, 282429536481, 2541865828329, 2541865828329, 22876792454961, 205891132094649, 5559060566555523, 50031545098999707

OFFSET

0,2

COMMENTS

Numerators are given under A120996.

See A120996 for details and a W. Lang link found there for the definition of four p-families of such scaled Catalan sums.

FORMULA

a(n)=denominator(r(n)) with r(n) := r(p=1,n) = sum(C(k)/L(2)^(2*k),k=0..n), with Lucas L(2)=3, and C(k):=A000108(k) (Catalan).

KEYWORD

nonn,frac,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 2006

STATUS

approved