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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A185585 Let f(n) = Sum_{j>=1} j^n/binomial(2*j,j) = r_n*Pi*sqrt(3)/3^{t_n} + s_n/3; sequence gives t_n. 3
3, 3, 4, 5, 5, 5, 6, 5, 7, 8, 8, 9, 10, 10, 10, 10, 8, 11, 12, 12, 13, 14, 14, 13, 15, 13, 16, 17, 17, 18, 19, 19, 19, 20, 19, 21, 22, 22, 23, 24, 24, 24, 24, 23, 24, 25, 25, 26, 27, 27, 26, 28, 26, 29, 30, 30, 31, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..57.

F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's Second Interesting Series, arXiv:1009.4274 [math-ph], 2010-2011.

F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's interesting series, Amer. Math. Monthly, 120 (2013), 116-130.

MAPLE

A185585:=proc(n)local j, x, y, z, tol;

x:=0; y:=1; j:=1;

tol:=100; #increase tol for very large value of n (n>50) or this may become inaccurate

while y>10^(-tol) do

y:=j^n/binomial(2*j, j);

x:=x+y; j:=j+1;

od:

return convert(evalf(log[3](denom(convert(evalf(((x-A098830[n]/3)/(Pi*sqrt(3)))), rational, tol-1)))), rational, 5);

end:

# Nathaniel Johnston, Apr 08 2011

MATHEMATICA

f[n_] := Sum[j^n/Binomial[2*j, j], {j, 1, Infinity}];

a[n_] := 1 + Log[3, Denominator[Expand[FunctionExpand[f[n]]][[2, 1]]]];

Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 60}] (* Jean-Fran├žois Alcover, Nov 24 2017 *)

CROSSREFS

Cf. A098830 (s_n), A181334 (r_n), A181374, A180875, A014307.

Sequence in context: A064631 A298200 A072648 * A072945 A307912 A274004

Adjacent sequences:  A185582 A185583 A185584 * A185586 A185587 A185588

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 09 2011, following a suggestion from Herb Conn

EXTENSIONS

a(11)-a(57) from Nathaniel Johnston, Apr 07 2011

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 26 05:23 EDT 2019. Contains 326328 sequences. (Running on oeis4.)