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A126963 Numerators of sequence defined by f(0)=1, f(1)=5/4; f(n) = (6n-1)*f(n-1)/(4n) - (2n-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

Table of n, a(n) for n=0..21.

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]

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 *)

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

CROSSREFS

Denominators are in A088802.

Sequence in context: A152866 A102851 A173554 * A221874 A182191 A038140

Adjacent sequences:  A126960 A126961 A126962 * A126964 A126965 A126966

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Mar 20 2007

STATUS

approved

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Last modified November 17 19:53 EST 2017. Contains 294834 sequences.