OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
EXAMPLE
a(3) = 729 because r(3) = 1 + 2/9 + 2/27 + 20/729 = 965/729 = A123749(3)/a(3).
MAPLE
seq(denom(add(binomial(2*k, k)/9^k, k = 0..n)), n = 0..20); # G. C. Greubel, Dec 25 2019
MATHEMATICA
Table[Denominator[Sum[(k+1)*CatalanNumber[k]/9^k, {k, 0, n}]], {n, 0, 20}] (* G. C. Greubel, Dec 25 2019 *)
PROG
(PARI) a(n) = denominator(sum(k=0, n, binomial(2*k, k)/9^k)); \\ Michel Marcus, Aug 12 2019
(Magma) [Denominator(&+[(k+1)*Catalan(k)/9^k: k in [0..n]]): n in [0..20]]; // G. C. Greubel, Dec 25 2019
(Sage) [denominator(sum((k+1)*catalan_number(k)/9^k for k in (0..n))) for n in (0..20)] # G. C. Greubel, Dec 25 2019
(GAP) List([0..20], n-> DenominatorRat(Sum([0..n], k-> Binomial(2*k, k)/9^k)) ); # G. C. Greubel, Dec 25 2019
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Nov 10 2006
STATUS
approved