A128507 Denominators of partial sums for a series for 3*sqrt(2)*(Pi^3)/2^7.

1, 27, 3375, 1157625, 31255875, 41601569625, 91398648466125, 91398648466125, 449041559914072125, 3079976059450620705375, 439996579921517243625, 5353438387905100303185375, 669179798488137537898171875

Offset: 0

Author

Wolfdieter Lang, Apr 04 2007

Keywords

• nonn
• frac
• easy

Comments

The numerators are given in A128506.

See the comments and the W. Lang link under A128506.

Examples

			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 ++--
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..385

Programs

Mathematica

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 *)

PARI

{r(n) = sum(k=0,n, ((1-I)*I^k + (1+I)*(-I)^k)/(2*(2*k+1)^3))};
for(n=0,30, print1(denominator(r(n)), ", ")) \\ G. C. Greubel, Mar 28 2018

Formula

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.