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A145560
Denominators of partial sums of a certain alternating series of inverse central binomial coefficients.
2
1, 12, 180, 5040, 8400, 831600, 75675600, 302702400, 15437822400, 293318625600, 248192683200, 74209612276800, 8388912692160, 964724959598400, 46628373047256000, 5781918257859744000, 10921401153735072000, 884633493452540832000, 621897345897136204896000
OFFSET
1,2
COMMENTS
See A145559 for the numerators, references and a W. Lang link.
LINKS
FORMULA
a(n) = (1/2)*denominator(r(n)), with the rationals (in lowest terms) r(n) := Sum_{k=1..n} (-1)^(k+1)/(binomial(2*k,k)*k^2).
EXAMPLE
Rationals r(n) (in lowest terms): [1/2, 11/24, 167/360, 4667/10080, 7781/16800, 770269/1663200, 70095379/151351200,...].
MAPLE
map(denom, ListTools:-PartialSums([seq(2*(-1)^(k+1)/(binomial(2*k, k)*k^2), k=1..30)])): # Robert Israel, Sep 24 2017
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Oct 13 2008
STATUS
approved