A130550 Denominators of partial sums for a series for 2*Zeta(2)/3 = (Pi^2)/9.

1, 12, 180, 1008, 8400, 118800, 75675600, 302702400, 15437822400, 26665329600, 3226504881600, 5708431713600, 964724959598400, 964724959598400, 46628373047256000, 340112838697632000, 98292610383615648000

Offset

1,2

Comments

Numerators are given in A130549.

For the rationals r(n):= 2*sum(1/(j^2*binomial(2*j,j)),j=1..n), n>=1, the van der Poorten reference and a W. Lang link see A130551.

Links

Table of n, a(n) for n=1..17.

C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.

Formula

a(n) = denominator(r(n)), n>=1.

Denominator of 2*Sum_{i=1..n} 1/(i^2*C(2*i,i)). - Wolfdieter Lang, Oct 07 2008, corrected by Vaclav Kotesovec, Mar 10 2016

Mathematica

Table[2*Sum[1/(i^2*Binomial[2*i, i]), {i, 1, n}], {n, 1, 20}] // Denominator (* Vaclav Kotesovec, Mar 10 2016 *)
(2Accumulate[Table[1/(n^2 Binomial[2n, n]), {n, 20}]])//Denominator (* Harvey P. Dale, Jan 27 2019 *)

Prog

(PARI) a(n) = denominator(2*sum(i=1, n, 1/(i^2*binomial(2*i, i)))); \\ Michel Marcus, Mar 10 2016

Crossrefs

Cf. A112099, A112100, A112102, A112103, A130549.

Sequence in context: A358951 A363152 A350541 * A073975 A069685 A000515

Adjacent sequences: A130547 A130548 A130549 * A130551 A130552 A130553

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Jul 13 2007

Status

approved