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%I #8 Mar 29 2018 02:44:58
%S 1,27,3375,1157625,31255875,41601569625,91398648466125,91398648466125,
%T 449041559914072125,3079976059450620705375,439996579921517243625,
%U 5353438387905100303185375,669179798488137537898171875
%N Denominators of partial sums for a series for 3*sqrt(2)*(Pi^3)/2^7.
%C The numerators are given in A128506.
%C See the comments and the W. Lang link under A128506.
%H G. C. Greubel, <a href="/A128507/b128507.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) = denominator(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 Rationals r(n): [1, 28/27, 3473/3375, 1187864/1157625, 32115203/31255875,...].
%e 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 r[n_]:= Sum[(1/2)*((1-I)*I^k+(1+I)*(-I)^k)/(2k+1)^3, {k,0,n}]; Denominator[Table[r[n], {n,0,30}]] (* _G. C. Greubel_, Mar 28 2018
%o (PARI) {r(n) = sum(k=0,n, ((1-I)*I^k + (1+I)*(-I)^k)/(2*(2*k+1)^3))};
%o for(n=0,30, print1(denominator(r(n)), ", ")) \\ _G. C. Greubel_, Mar 28 2018
%K nonn,frac,easy
%O 0,2
%A _Wolfdieter Lang_, Apr 04 2007
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