Search: id:A128506
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%I A128506
%S A128506 1,28,3473,1187864,32115203,42776591068,93938569006771,93911487925744,
%T A128506 461478538827646397,3165730339378740709148,452199680641199918039,
%U A128506 5501473517781557885536888,687727017229797976494536483
%N A128506 Numerators of partial sums for a series for 3*sqrt(2)*(Pi^3)/2^7.
%C A128506 The denominators are given in A128507.
%C A128506 The limit n -> infinity of the rationals r(n) defined below is 3*sqrt(2)*(Pi^3)/
               2^7 = 1.027756...
%C A128506 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.
%H A128506 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A128506.text">
               Rationals and limit.</a>
%F A128506 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.
%e A128506 Rationals r(n): [1, 28/27, 3473/3375, 1187864/1157625, 32115203/31255875,
               ...].
%e A128506 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 + ...
%Y A128506 Sequence in context: A103660 A107444 A061787 this_sequence A164655 A036525 
               A131315
%Y A128506 Adjacent sequences: A128503 A128504 A128505 this_sequence A128507 A128508 
               A128509
%K A128506 nonn,frac,easy
%O A128506 0,2
%A A128506 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Apr 04 2007

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