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 A089639 Denominator of (5/2)*Sum_{i=1..n} (-1)^(i-1)/(i^3*C(2*i,i)). 1
 1, 4, 96, 864, 48384, 1209600, 5702400, 25427001600, 203416012800, 31122649958400, 53757304473600, 71550972254361600, 7446481275340800, 278118629152703539200, 278118629152703539200, 40327201227142013184000, 588302700254777604096000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Related to Apery's proof of the irrationality of zeta(3). LINKS Table of n, a(n) for n=0..16. C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45. FORMULA (5/2)*Sum_{i >= 1} (-1)^(i-1)/(i^3*C(2*i, i)) = zeta(3). EXAMPLE 0, 5/4, 115/96, 1039/864, 58157/48384, 1454021/1209600, 6854599/5702400, ... -> zeta(3). MATHEMATICA Denominator[Table[5/2 Sum[(-1)^(i-1)/(i^3 Binomial[2i, i]), {i, n}], {n, 0, 20}]] (* Harvey P. Dale, Aug 25 2012 *) PROG (PARI) a(n)=denominator(5/2*sum(k=1, n, (-1)^(k+1)/k^3/binomial(2*k, k))) CROSSREFS Cf. A002117, A089638. Sequence in context: A203316 A359653 A202682 * A269091 A204973 A204700 Adjacent sequences: A089636 A089637 A089638 * A089640 A089641 A089642 KEYWORD nonn,frac AUTHOR Benoit Cloitre, Jan 01 2004 EXTENSIONS Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified September 16 23:59 EDT 2024. Contains 375984 sequences. (Running on oeis4.)