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A060851
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a(n) = (2n-1) * 3^(2n-1).
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4
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3, 81, 1215, 15309, 177147, 1948617, 20726199, 215233605, 2195382771, 22082967873, 219667417263, 2165293113021, 21182215236075, 205891132094649, 1990280943581607, 19147875284802357, 183448998696332259, 1751104078464989745, 16660504517966902431
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OFFSET
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1,1
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COMMENTS
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Denominators of odd terms in expansion of arctanh(s/3); numerators are all 1. - Gerry Martens, Jul 26 2015
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 28-40.
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LINKS
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FORMULA
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Sum_{n>=1} 2/a(n) = log(2).
Sum_{n>=1} (2/a(n) - zeta(2n+1)/(2^(2n)*(2n+1))) = gamma (Euler's constant).
Sum_{n>=1} ((4n+2)/a(n) - zeta(2n+1)/2^(2n))/(2n+1) = gamma (Euler's constant).
Sum_{n>=1} ((4n+2)/a(n) - zeta(2n+1)/2^(2n)) = 7/4.
Sum_{n>=1} ((2n+1)/a(n) - zeta(2n+1)/2^(2n+1)) = 7/8.
G.f.: 3*x*(1+9*x) / (9*x-1)^2.
Sum_{n>=1} (-1)^(n+1)/a(n) = arctan(1/3). - Amiram Eldar, Feb 26 2022
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MAPLE
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MATHEMATICA
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a[n_] := 1/SeriesCoefficient[ArcTanh[s/3], {s, 0, n}]
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PROG
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(PARI) for (n=1, 200, write("b060851.txt", n, " ", (2*n - 1)*(3^(2*n - 1))); ) \\ Harry J. Smith, Jul 13 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001
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STATUS
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approved
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