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A130550
Denominators of partial sums for a series for 2*Zeta(2)/3 = (Pi^2)/9.
5
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.
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
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Jul 13 2007
STATUS
approved