A084224 Denominators of successive approximations to zeta(3) = Sum_{k>0} 1/k^3, using Zeilberger's formula with s=2.

24, 1728, 324000, 19559232000, 208039104000, 181050031008000, 1889392861091736000, 32719838723847475200, 126909921829154720256000, 25243779460958994560841216000

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..328

D. Zeilberger, Faster and Faster convergent series for zeta(3), arXiv:math/9804126 [math.CO], 1998.

Formula

a(n) = denominator( Sum_{k=1..n} (1/4)*(-1)^(k-1)*(56*k^2-32*k+5)/((2*k-1)^2 * binomial(3*k,k) * binomial(2*k,k) * k^3) ). - G. C. Greubel, Oct 08 2018

Maple

a:=n->add((1/4)*(-1)^(k-1)*(56*k^2-32*k+5)/((2*k-1)^2*binomial(3*k, k)*binomial(2*k, k)*k^3), k=1..n): seq(denom(a(n)), n=1..10); # Muniru A Asiru, Oct 09 2018

Mathematica

Table[Denominator[Sum[(1/4)*(-1)^(k-1)*(56*k^2-32*k+5)/((2*k-1)^2*Binomial[3*k, k]* Binomial[2*k, k]*k^3), {k, 1, n}]], {n, 1, 30}] (* G. C. Greubel, Oct 08 2018 *)

Prog

(PARI) for(n=1, 15, print1(denominator(sum(k=1, n, (1/4)*(-1)^(k-1)*(56*k^2 -32*k +5)/((2*k-1)^2*binomial(3*k, k) *binomial(2*k, k)*k^3))), ", "))
(Magma) [Denominator((&+[(1/4)*(-1)^(k-1)*(56*k^2-32*k+5)/((2*k-1)^2*Binomial(3*k, k)*Binomial(2*k, k)*k^3): k in [1..n]])): n in [1..30]]; // G. C. Greubel, Oct 08 2018
(GAP) List(List([1..10], n->Sum([1..n], k->(1/4)*(-1)^(k-1)*(56*k^2-32*k+5)/((2*k-1)^2*Binomial(3*k, k)*Binomial(2*k, k)*k^3))), DenominatorRat); # Muniru A Asiru, Oct 09 2018

Crossrefs

Numerators are in A084223, decimal expansion is in A002117.

Sequence in context: A229430 A054777 A301392 * A348589 A227257 A222999

Adjacent sequences: A084221 A084222 A084223 * A084225 A084226 A084227

Keyword

nonn,frac

Author

Ralf Stephan, May 19 2003

Status

approved