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 A053005 Denominator of beta(2n+1)/Pi^(2n+1), where beta(m) = Sum_{k=0..inf} (-1)^k/(2k+1)^m. 2
 4, 32, 1536, 184320, 8257536, 14863564800, 1569592442880, 5713316492083200, 1096956766479974400, 6713375410857443328000, 408173224980132554342400, 18857602994082124010618880000, 640578267860512766391484416000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 384, Problem 15. L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Problem 37, beta(n). LINKS T. D. Noe, Table of n, a(n) for n = 0..100 Eric Weisstein's World of Mathematics, Dirichlet Beta Function EXAMPLE beta(5) = 5*Pi^5/1536 so a(2)=1536. MATHEMATICA beta[1] = Pi/4; beta[m_] := (Zeta[m, 1/4] - Zeta[m, 3/4])/4^m; a[n_, p_] := a[n, p] = beta[2*n+1]/Pi^(2*n+1) // N[#, p]& // Rationalize[#, 0]& // Denominator; a[n_] := Module[{p = 16}, a[n, p]; p = 2*p; While[a[n, p] != a[n, p/2], p = 2*p]; a[n, p]]; Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Aug 19 2013 *) CROSSREFS Cf. A046976. Sequence in context: A231991 A028369 A081790 * A257583 A258122 A012092 Adjacent sequences: A053002 A053003 A053004 * A053006 A053007 A053008 KEYWORD nonn,frac,nice,easy AUTHOR N. J. A. Sloane, Feb 21 2000 STATUS approved

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Last modified December 6 21:00 EST 2022. Contains 358648 sequences. (Running on oeis4.)