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 A262177 Decimal expansion of Q_5 = zeta(5) / (Sum_{k>=1} (-1)^(k+1) / (k^5 * binomial(2k, k))), a conjecturally irrational constant defined by an Apéry-like formula. 34
 2, 0, 9, 4, 8, 6, 8, 6, 2, 2, 0, 1, 0, 0, 3, 6, 9, 9, 3, 8, 5, 0, 2, 4, 9, 2, 9, 3, 7, 3, 2, 9, 4, 1, 6, 3, 0, 2, 9, 6, 7, 5, 8, 7, 4, 8, 5, 6, 7, 7, 8, 1, 8, 2, 7, 4, 0, 1, 2, 7, 5, 8, 7, 8, 3, 7, 4, 3, 8, 0, 0, 7, 8, 7, 6, 8, 4, 6, 8, 1, 5, 6, 3, 2, 0, 6, 0, 4, 4, 2, 3, 2, 0, 9, 0, 4, 3, 1, 3, 6, 9, 3, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The similar constant Q_3 = zeta(3) / (Sum_{k>=1} (-1)^(k+1) / (k^3 * binomial(2k, k))) evaluates to 5/2. LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 David Bailey, Jonathan Borwein, David Bradley, Experimental determination of Apéry-like identities for zeta(2n+2), arXiv:math/0505270 [math.NT], 2005. FORMULA Equals 2*zeta(5)/6F5(1,1,1,1,1,1; 3/2,2,2,2,2; -1/4). EXAMPLE 2.09486862201003699385024929373294163029675874856778182740127587837438... MATHEMATICA Q5 = Zeta[5]/Sum[(-1)^(k+1)/(k^5*Binomial[2k, k]), {k, 1, Infinity}]; RealDigits[Q5, 10, 103] // First PROG (PARI) zeta(5)/suminf(k=1, (-1)^(k+1)/(k^5*binomial(2*k, k))) \\ Michel Marcus, Sep 14 2015 CROSSREFS Cf. A013663. The Apéry-like numbers [or Apéry-like sequences, Apery-like numbers, Apery-like sequences] include A000172, A000984, A002893, A002895, A005258, A005259, A005260, A006077, A036917, A063007, A081085, A093388, A125143 (apart from signs), A143003, A143007, A143413, A143414, A143415, A143583, A183204, A214262, A219692, A226535, A227216, A227454, A229111 (apart from signs), A260667, A260832, A262177, A264541, A264542, A279619, A290575, A290576. (The term "Apery-like" is not well-defined.) Sequence in context: A168229 A019693 A007493 * A136319 A176057 A272413 Adjacent sequences:  A262174 A262175 A262176 * A262178 A262179 A262180 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Sep 14 2015 STATUS approved

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Last modified October 21 22:13 EDT 2018. Contains 316429 sequences. (Running on oeis4.)