The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A126963 Numerators of sequence defined by f(0)=1, f(1)=5/4; f(n) = ( (6*n-1)*f(n-1) - (2*n-1)*f(n-2) )/(4n). 2
 1, 5, 43, 177, 2867, 11531, 92479, 370345, 11857475, 47442055, 379582629, 1518418695, 24295375159, 97182800711, 777467420263, 3109879375897, 199032580597603, 796130905791967, 6369049515119561, 25476202478636219, 407619274119811709, 1630477163761481141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..500 D. Doster, Problem 1318, Three Term Recurrence, Math. Magazine, 63 (1990), 127-128. FORMULA f(n) = Sum_{k=0..n} binomial(-1/2,k)*(-1/2)^k. f(n) -> sqrt(2) as n -> oo. G.f.: (sqrt(-x)*arccsc(1-x)/sqrt(2)-(Pi*i*sqrt(x))/sqrt(2)^3)/x. - Vladimir Kruchinin, Oct 10 2012 a(n) = numerator( Sum_{k=0..n} binomial(2*k, k)/8^k ). - G. C. Greubel, Jan 29 2020 MAPLE seq( numer( add(binomial(2*k, k)/8^k, k=0..n) ), n=0..25); # G. C. Greubel, Jan 29 2020 MATHEMATICA a[n_] := Sqrt[2](1-(Gamma[1/2+n] Hypergeometric2F1[n, 1/2+n, 1+n, -1])/(Sqrt[Pi] Gamma[1+n])); Table[Numerator[FullSimplify[a[n]]], {n, 20}] (* Gerry Martens, Aug 09 2015 *) f[n_]:= If[n==0, 1, If[n==1, 5/4, ((6*n-1)*f[n-1]-(2*n-1)*f[n-2])/(4*n)]]; Table[Numerator[f[n]], {n, 0, 25}] (* G. C. Greubel, Jan 29 2020 *) PROG (PARI) A126963(n)=numerator(sum(k=0, n, binomial(-1/2, k)/(-2)^k)) \\ f(n)=if(n>1, ((6*n-1)*f(n-1)-(2*n-1)*f(n-2))/(4*n), (5/4)^n) yields the same results. - M. F. Hasler, Aug 11 2015 (Magma) [Numerator( &+[Binomial(2*k, k)/8^k: k in [0..n]] ): n in [0..25]]; // G. C. Greubel, Jan 29 2020 (Sage) [numerator( sum(binomial(2*k, k)/8^k for k in (0..n)) ) for n in (0..25)] # G. C. Greubel, Jan 29 2020 (GAP) List([0..25], n-> NumeratorRat( Sum([0..n], k-> Binomial(2*k, k)/8^k) )); # G. C. Greubel, Jan 29 2020 CROSSREFS Denominators are in A088802. Sequence in context: A152866 A102851 A173554 * A221874 A317282 A182191 Adjacent sequences: A126960 A126961 A126962 * A126964 A126965 A126966 KEYWORD nonn,frac AUTHOR N. J. A. Sloane, Mar 20 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)