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!)
A128506 Numerators of partial sums for a series for 3*sqrt(2)*(Pi^3)/2^7. 3
1, 28, 3473, 1187864, 32115203, 42776591068, 93938569006771, 93911487925744, 461478538827646397, 3165730339378740709148, 452199680641199918039, 5501473517781557885536888, 687727017229797976494536483 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The denominators are given in A128507.

The limit n -> infinity of the rationals r(n) defined below is 3*sqrt(2)*(Pi^3)/2^7 = 1.027756...

This series is obtained from the Fourier series for y(x)= x*(Pi-x) if 0<=x<=Pi and y(x)= (Pi-x)*(2*Pi-x) if Pi<=x<=2*Pi evaluated at x=Pi/4.

LINKS

Table of n, a(n) for n=0..12.

W. Lang, Rationals and limit.

FORMULA

a(n)=numerator(r(n)) with the rationals r(n):=sum(S(2*k,sqrt(2))/(2*k+1)^3,k=0..n) with Chebyshev's S-Polynomials S(2*k,sqrt(2))=[1,1,-1,-1] periodic sequence with period 4. See A057077.

EXAMPLE

Rationals r(n): [1, 28/27, 3473/3375, 1187864/1157625, 32115203/31255875,...].

3*sqrt(2)*(Pi^3)/2^7 = 1/1^3 + 1/3^3 - 1/5^3 - 1/7^3 + 1/9^3 + 1/11^3 - 1/13^3 - 1/15^3 + ...

CROSSREFS

Sequence in context: A232520 A061787 A235458 * A164655 A242449 A201099

Adjacent sequences:  A128503 A128504 A128505 * A128507 A128508 A128509

KEYWORD

nonn,frac,easy

AUTHOR

Wolfdieter Lang Apr 04 2007

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 7 13:07 EST 2016. Contains 278875 sequences.