OFFSET
0,2
COMMENTS
Denominators are given by A123748.
The sum over central binomial coefficients scaled by powers of 5, r(n) = Sum_{k=0..n} binomial(2*k,k)/5^k, has the limit lim_{n -> infinity} r(n) = sqrt(5). From the expansion of 1/sqrt(1-x) for x=4/5.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Wolfdieter Lang, Rationals and more.
FORMULA
EXAMPLE
a(3)=9 because r(3)= 1+2/5+6/25+4/25 = 9/5 = a(3)/A123748(3).
MAPLE
A123747:=n-> numer(sum(binomial(2*k, k)/5^k, k=0..n)); seq(A123747(n), n=0..25); # G. C. Greubel, Aug 10 2019
MATHEMATICA
Table[Numerator[Sum[Binomial[2*k, k]/5^k, {k, 0, n}]], {n, 0, 25}] (* G. C. Greubel, Aug 10 2019 *)
PROG
(PARI) vector(25, n, n--; numerator(sum(k=0, n, binomial(2*k, k)/5^k))) \\ G. C. Greubel, Aug 10 2019
(Magma) [Numerator( (&+[Binomial(2*k, k)/5^k: k in [0..n]])): n in [0..25]]; // G. C. Greubel, Aug 10 2019
(Sage) [numerator( sum(binomial(2*k, k)/5^k for k in (0..n)) ) for n in (0..25)] # G. C. Greubel, Aug 10 2019
(GAP) List([0..25], n-> NumeratorRat(Sum([0..n], k-> Binomial(2*k, k)/5^k )) ); # G. C. Greubel, Aug 10 2019
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Nov 10 2006
STATUS
approved