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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

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Last modified July 31 09:25 EDT 2014. Contains 245083 sequences.