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 A060851 a(n) = (2n-1) * 3^(2n-1). 2
 3, 81, 1215, 15309, 177147, 1948617, 20726199, 215233605, 2195382771, 22082967873, 219667417263, 2165293113021, 21182215236075, 205891132094649, 1990280943581607, 19147875284802357, 183448998696332259, 1751104078464989745, 16660504517966902431 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Denominators of odd terms in expansion of arctanh(s/3); numerators are all 1. - Gerry Martens, Jul 26 2015 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 28-40. LINKS Harry J. Smith, Table of n, a(n) for n = 1..200 Xavier Gourdon and Pascal Sebah, Riemann's zeta function Pablo A. Panzone, Formulas for the Euler-Mascheroni constant, Rev. Un. Mat. Argentina, Vol 50, No. 1 (2009), pp. 161-164. Simon Plouffe, Other interesting computations Index entries for linear recurrences with constant coefficients, signature (18,-81) FORMULA From R. J. Mathar, May 07 2013: (Start) G.f.: 3*x*(1+9*x) / (9*x-1)^2. a(n+1) = 3*A155988(n). (End) EXAMPLE Log(2) = sum( 2 / a(n)) for n = 1..infinity. C0 = sum( 2 / a(n) - zeta(2n+1) / [ ( 2^(2n)) * (2n+1) ] ). C0 = sum( [ (4n+2) / a(n) - zeta(2n+1) / (2^(2n)) ] / (2n+1)). 7/4= sum( [ (4n+2) / a(n) - zeta(2n+1) / (2^(2n)) ] ). 7/8= sum( [ (2n+1) / a(n) - zeta(2n+1) / (2^(2n+1)) ] ). MAPLE A060851:=n->(2*n-1)*3^(2*n-1); seq(A060851(n), n=1..20); # Wesley Ivan Hurt, Dec 02 2013 MATHEMATICA Table[(2*n - 1)*3^(2*n - 1), {n, 20}] (* Wesley Ivan Hurt, Dec 02 2013 *) a[n_] := 1/SeriesCoefficient[ArcTanh[s/3], {s, 0, n}] Table[a[n], {n, 1, 40, 2}] (* Gerry Martens, Jul 26 2015 *) PROG (PARI) for (n=1, 200, write("b060851.txt", n, " ", (2*n - 1)*(3^(2*n - 1))); ) \\ Harry J. Smith, Jul 13 2009 (MAGMA) [ (2*n-1) * (3^(2*n-1)): n in [1..100]]; // Vincenzo Librandi, Apr 20 2011 CROSSREFS For log(2) see A002162, for Euler's constant C0 see A001620. Sequence in context: A123656 A229842 A223187 * A116179 A013732 A209587 Adjacent sequences:  A060848 A060849 A060850 * A060852 A060853 A060854 KEYWORD nonn,easy AUTHOR Frank Ellermann, May 03 2001 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001 STATUS approved

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Last modified December 2 12:56 EST 2016. Contains 278678 sequences.