This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A128506 #19 Sep 20 2024 03:37:48
%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 G. C. Greubel, <a href="/A128506/b128506.txt">Table of n, a(n) for n = 0..385</a>
%H A128506 W. Lang, <a href="/A128506/a128506.txt">Rationals and limit.</a>
%F A128506 a(n) = numerator(r(n)) with the rationals r(n) = Sum_{k=0..n} S(2*k,sqrt(2))/(2*k+1)^3 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 + ...
%t A128506 r[n_]:= Sum[(1/2)*((1-I)*I^k+(1+I)*(-I)^k)/(2k+1)^3, {k,0,n}]; Numerator[Table[r[n], {n,0,30}]] (* _G. C. Greubel_, Mar 28 2018 *)
%o A128506 (PARI) {r(n) = sum(k=0,n, ((1-I)*I^k + (1+I)*(-I)^k)/(2*(2*k+1)^3))};
%o A128506 for(n=0,30, print1(numerator(r(n)), ", ")) \\ _G. C. Greubel_, Mar 28 2018
%K A128506 nonn,frac,easy
%O A128506 0,2
%A A128506 _Wolfdieter Lang_, Apr 04 2007