login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

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