OFFSET
0,2
COMMENTS
Denominators are given by A124396.
The sums over central binomial coefficients scaled by powers of 9, r(n) = Sum_{k=0..n} binomial(2*k,k)/9^k have the limit s = lim_{n->infinity} r(n) = 3/sqrt(5). From the expansion of 1/sqrt(1-x) for x=4/9.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Wolfdieter Lang, Rationals and more.
FORMULA
EXAMPLE
a(3) = 965 because r(3) = 1 + 2/9 + 2/27 + 20/729 = 965/729 = a(3)/A124396(3).
MAPLE
A123749:=n-> numer(sum(binomial(2*k, k)/9^k, k=0..n)); seq(A123749(n), n=0..20); # G. C. Greubel, Aug 10 2019
MATHEMATICA
Table[Numerator[Sum[Binomial[2*k, k]/9^k, {k, 0, n}]], {n, 0, 20}] (* G. C. Greubel, Aug 10 2019 *)
PROG
(PARI) vector(20, n, n--; numerator(sum(k=0, n, binomial(2*k, k)/9^k))) \\ G. C. Greubel, Aug 10 2019
(Magma) [Numerator( (&+[Binomial(2*k, k)/9^k: k in [0..n]])): n in [0..20]]; // G. C. Greubel, Aug 10 2019
(Sage) [numerator( sum(binomial(2*k, k)/9^k for k in (0..n)) ) for n in (0..20)] # G. C. Greubel, Aug 10 2019
(GAP) List([0..20], n-> NumeratorRat(Sum([0..n], k-> Binomial(2*k, k)/9^k )) ); # G. C. Greubel, Aug 10 2019
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Nov 10 2006
STATUS
approved